Finite Math Examples

$250 x + 450 y = 4190$ , $301 x + 390 y = 3700$ , $382 x + 289 y = 4404$

Step 1

Solve for $x$ in $250 x + 450 y = 4190$ .

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Step 1.1

Subtract $450 y$ from both sides of the equation.

$250 x = 4190 - 450 y$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

Step 1.2

Divide each term in $250 x = 4190 - 450 y$ by $250$ and simplify.

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Step 1.2.1

Divide each term in $250 x = 4190 - 450 y$ by $250$ .

$\frac{250 x}{250} = \frac{4190}{250} + \frac{- 450 y}{250}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $250$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{250 x}{250} = \frac{4190}{250} + \frac{- 450 y}{250}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{4190}{250} + \frac{- 450 y}{250}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

$x = \frac{4190}{250} + \frac{- 450 y}{250}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

$x = \frac{4190}{250} + \frac{- 450 y}{250}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Cancel the common factor of $4190$ and $250$ .

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Step 1.2.3.1.1.1

Factor $10$ out of $4190$ .

$x = \frac{10 (419)}{250} + \frac{- 450 y}{250}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $10$ out of $250$ .

$x = \frac{10 \cdot 419}{10 \cdot 25} + \frac{- 450 y}{250}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$x = \frac{10 \cdot 419}{10 \cdot 25} + \frac{- 450 y}{250}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$x = \frac{419}{25} + \frac{- 450 y}{250}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

$x = \frac{419}{25} + \frac{- 450 y}{250}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

$x = \frac{419}{25} + \frac{- 450 y}{250}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

Step 1.2.3.1.2

Cancel the common factor of $- 450$ and $250$ .

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Step 1.2.3.1.2.1

Factor $50$ out of $- 450 y$ .

$x = \frac{419}{25} + \frac{50 (- 9 y)}{250}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $50$ out of $250$ .

$x = \frac{419}{25} + \frac{50 (- 9 y)}{50 (5)}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$x = \frac{419}{25} + \frac{50 (- 9 y)}{50 \cdot 5}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$x = \frac{419}{25} + \frac{- 9 y}{5}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

$x = \frac{419}{25} + \frac{- 9 y}{5}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

$x = \frac{419}{25} + \frac{- 9 y}{5}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$x = \frac{419}{25} - \frac{9 y}{5}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

$x = \frac{419}{25} - \frac{9 y}{5}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

$x = \frac{419}{25} - \frac{9 y}{5}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

$x = \frac{419}{25} - \frac{9 y}{5}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

$x = \frac{419}{25} - \frac{9 y}{5}$

$301 x + 390 y = 3700$

$382 x + 289 y = 4404$

Step 2

Replace all occurrences of $x$ with $\frac{419}{25} - \frac{9 y}{5}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $301 x + 390 y = 3700$ with $\frac{419}{25} - \frac{9 y}{5}$ .

$301 (\frac{419}{25} - \frac{9 y}{5}) + 390 y = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $301 (\frac{419}{25} - \frac{9 y}{5}) + 390 y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$301 (\frac{419}{25}) + 301 (- \frac{9 y}{5}) + 390 y = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.1.2

Multiply $301 (\frac{419}{25})$ .

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Step 2.2.1.1.2.1

Combine $301$ and $\frac{419}{25}$ .

$\frac{301 \cdot 419}{25} + 301 (- \frac{9 y}{5}) + 390 y = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.1.2.2

Multiply $301$ by $419$ .

$\frac{126119}{25} + 301 (- \frac{9 y}{5}) + 390 y = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

$\frac{126119}{25} + 301 (- \frac{9 y}{5}) + 390 y = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.1.3

Multiply $301 (- \frac{9 y}{5})$ .

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Step 2.2.1.1.3.1

Multiply $- 1$ by $301$ .

$\frac{126119}{25} - 301 \frac{9 y}{5} + 390 y = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.1.3.2

Combine $- 301$ and $\frac{9 y}{5}$ .

$\frac{126119}{25} + \frac{- 301 (9 y)}{5} + 390 y = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.1.3.3

Multiply $9$ by $- 301$ .

$\frac{126119}{25} + \frac{- 2709 y}{5} + 390 y = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

$\frac{126119}{25} + \frac{- 2709 y}{5} + 390 y = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.1.4

Move the negative in front of the fraction.

$\frac{126119}{25} - \frac{2709 y}{5} + 390 y = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

$\frac{126119}{25} - \frac{2709 y}{5} + 390 y = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.2

To write $390 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{126119}{25} - \frac{2709 y}{5} + 390 y \cdot \frac{5}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.3

Simplify terms.

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Step 2.2.1.3.1

Combine $390 y$ and $\frac{5}{5}$ .

$\frac{126119}{25} - \frac{2709 y}{5} + \frac{390 y \cdot 5}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.3.2

Combine the numerators over the common denominator.

$\frac{126119}{25} + \frac{- 2709 y + 390 y \cdot 5}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

$\frac{126119}{25} + \frac{- 2709 y + 390 y \cdot 5}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.4

Simplify each term.

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Step 2.2.1.4.1

Simplify the numerator.

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Step 2.2.1.4.1.1

Factor $3 y$ out of $- 2709 y + 390 y \cdot 5$ .

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Step 2.2.1.4.1.1.1

Factor $3 y$ out of $- 2709 y$ .

$\frac{126119}{25} + \frac{3 y (- 903) + 390 y \cdot 5}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.4.1.1.2

Factor $3 y$ out of $390 y \cdot 5$ .

$\frac{126119}{25} + \frac{3 y (- 903) + 3 y (130 \cdot 5)}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.4.1.1.3

Factor $3 y$ out of $3 y (- 903) + 3 y (130 \cdot 5)$ .

$\frac{126119}{25} + \frac{3 y (- 903 + 130 \cdot 5)}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

$\frac{126119}{25} + \frac{3 y (- 903 + 130 \cdot 5)}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.4.1.2

Multiply $130$ by $5$ .

$\frac{126119}{25} + \frac{3 y (- 903 + 650)}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.4.1.3

Add $- 903$ and $650$ .

$\frac{126119}{25} + \frac{3 y \cdot - 253}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.4.1.4

Multiply $- 253$ by $3$ .

$\frac{126119}{25} + \frac{- 759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

$\frac{126119}{25} + \frac{- 759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.2.1.4.2

Move the negative in front of the fraction.

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$382 x + 289 y = 4404$

Step 2.3

Replace all occurrences of $x$ in $382 x + 289 y = 4404$ with $\frac{419}{25} - \frac{9 y}{5}$ .

$382 (\frac{419}{25} - \frac{9 y}{5}) + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $382 (\frac{419}{25} - \frac{9 y}{5}) + 289 y$ .

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Step 2.4.1.1

Simplify each term.

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Step 2.4.1.1.1

Apply the distributive property.

$382 (\frac{419}{25}) + 382 (- \frac{9 y}{5}) + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.1.2

Multiply $382 (\frac{419}{25})$ .

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Step 2.4.1.1.2.1

Combine $382$ and $\frac{419}{25}$ .

$\frac{382 \cdot 419}{25} + 382 (- \frac{9 y}{5}) + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.1.2.2

Multiply $382$ by $419$ .

$\frac{160058}{25} + 382 (- \frac{9 y}{5}) + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{160058}{25} + 382 (- \frac{9 y}{5}) + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.1.3

Multiply $382 (- \frac{9 y}{5})$ .

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Step 2.4.1.1.3.1

Multiply $- 1$ by $382$ .

$\frac{160058}{25} - 382 \frac{9 y}{5} + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.1.3.2

Combine $- 382$ and $\frac{9 y}{5}$ .

$\frac{160058}{25} + \frac{- 382 (9 y)}{5} + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.1.3.3

Multiply $9$ by $- 382$ .

$\frac{160058}{25} + \frac{- 3438 y}{5} + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{160058}{25} + \frac{- 3438 y}{5} + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.1.4

Move the negative in front of the fraction.

$\frac{160058}{25} - \frac{3438 y}{5} + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{160058}{25} - \frac{3438 y}{5} + 289 y = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.2

To write $289 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{160058}{25} - \frac{3438 y}{5} + 289 y \cdot \frac{5}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.3

Simplify terms.

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Step 2.4.1.3.1

Combine $289 y$ and $\frac{5}{5}$ .

$\frac{160058}{25} - \frac{3438 y}{5} + \frac{289 y \cdot 5}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.3.2

Combine the numerators over the common denominator.

$\frac{160058}{25} + \frac{- 3438 y + 289 y \cdot 5}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{160058}{25} + \frac{- 3438 y + 289 y \cdot 5}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.4

Simplify each term.

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Step 2.4.1.4.1

Simplify the numerator.

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Step 2.4.1.4.1.1

Factor $y$ out of $- 3438 y + 289 y \cdot 5$ .

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Step 2.4.1.4.1.1.1

Factor $y$ out of $- 3438 y$ .

$\frac{160058}{25} + \frac{y \cdot - 3438 + 289 y \cdot 5}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.4.1.1.2

Factor $y$ out of $289 y \cdot 5$ .

$\frac{160058}{25} + \frac{y \cdot - 3438 + y (289 \cdot 5)}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.4.1.1.3

Factor $y$ out of $y \cdot - 3438 + y (289 \cdot 5)$ .

$\frac{160058}{25} + \frac{y (- 3438 + 289 \cdot 5)}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{160058}{25} + \frac{y (- 3438 + 289 \cdot 5)}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.4.1.2

Multiply $289$ by $5$ .

$\frac{160058}{25} + \frac{y (- 3438 + 1445)}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.4.1.3

Add $- 3438$ and $1445$ .

$\frac{160058}{25} + \frac{y \cdot - 1993}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{160058}{25} + \frac{y \cdot - 1993}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.4.2

Move $- 1993$ to the left of $y$ .

$\frac{160058}{25} + \frac{- 1993 \cdot y}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 2.4.1.4.3

Move the negative in front of the fraction.

$\frac{160058}{25} - \frac{1993 y}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{160058}{25} - \frac{1993 y}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{160058}{25} - \frac{1993 y}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{160058}{25} - \frac{1993 y}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{160058}{25} - \frac{1993 y}{5} = 4404$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3

Solve for $y$ in $\frac{160058}{25} - \frac{1993 y}{5} = 4404$ .

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Step 3.1

Move all terms not containing $y$ to the right side of the equation.

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Step 3.1.1

Subtract $\frac{160058}{25}$ from both sides of the equation.

$- \frac{1993 y}{5} = 4404 - \frac{160058}{25}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.1.2

To write $4404$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$- \frac{1993 y}{5} = 4404 \cdot \frac{25}{25} - \frac{160058}{25}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.1.3

Combine $4404$ and $\frac{25}{25}$ .

$- \frac{1993 y}{5} = \frac{4404 \cdot 25}{25} - \frac{160058}{25}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.1.4

Combine the numerators over the common denominator.

$- \frac{1993 y}{5} = \frac{4404 \cdot 25 - 160058}{25}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Multiply $4404$ by $25$ .

$- \frac{1993 y}{5} = \frac{110100 - 160058}{25}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.1.5.2

Subtract $160058$ from $110100$ .

$- \frac{1993 y}{5} = \frac{- 49958}{25}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$- \frac{1993 y}{5} = \frac{- 49958}{25}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.1.6

Move the negative in front of the fraction.

$- \frac{1993 y}{5} = - \frac{49958}{25}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$- \frac{1993 y}{5} = - \frac{49958}{25}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.2

Multiply both sides of the equation by $- \frac{5}{1993}$ .

$- \frac{5}{1993} \cdot (- \frac{1993 y}{5}) = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $- \frac{5}{1993} (- \frac{1993 y}{5})$ .

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Step 3.3.1.1.1

Cancel the common factor of $5$ .

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Step 3.3.1.1.1.1

Move the leading negative in $- \frac{5}{1993}$ into the numerator.

$\frac{- 5}{1993} \cdot (- \frac{1993 y}{5}) = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.1.1.1.2

Move the leading negative in $- \frac{1993 y}{5}$ into the numerator.

$\frac{- 5}{1993} \cdot \frac{- 1993 y}{5} = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{1993} \cdot \frac{- 1993 y}{5} = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{1993} \cdot \frac{- 1993 y}{5} = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{1993} \cdot (- 1993 y) = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{- 1}{1993} \cdot (- 1993 y) = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.1.1.2

Cancel the common factor of $1993$ .

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Step 3.3.1.1.2.1

Factor $1993$ out of $- 1993 y$ .

$\frac{- 1}{1993} \cdot (1993 (- y)) = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{1993} \cdot (1993 (- y)) = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.1.1.2.3

Rewrite the expression.

$y = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$y = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.1.1.3

Multiply.

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Step 3.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$y = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$y = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$y = - \frac{5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $- \frac{5}{1993} (- \frac{49958}{25})$ .

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Step 3.3.2.1.1

Cancel the common factor of $5$ .

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Step 3.3.2.1.1.1

Move the leading negative in $- \frac{5}{1993}$ into the numerator.

$y = \frac{- 5}{1993} \cdot (- \frac{49958}{25})$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.2.1.1.2

Move the leading negative in $- \frac{49958}{25}$ into the numerator.

$y = \frac{- 5}{1993} \cdot \frac{- 49958}{25}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.2.1.1.3

Factor $5$ out of $- 5$ .

$y = \frac{5 (- 1)}{1993} \cdot \frac{- 49958}{25}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.2.1.1.4

Factor $5$ out of $25$ .

$y = \frac{5 \cdot - 1}{1993} \cdot \frac{- 49958}{5 \cdot 5}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.2.1.1.5

Cancel the common factor.

$y = \frac{5 \cdot - 1}{1993} \cdot \frac{- 49958}{5 \cdot 5}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.2.1.1.6

Rewrite the expression.

$y = \frac{- 1}{1993} \cdot \frac{- 49958}{5}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$y = \frac{- 1}{1993} \cdot \frac{- 49958}{5}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.2.1.2

Multiply $\frac{- 1}{1993}$ by $\frac{- 49958}{5}$ .

$y = \frac{49958}{1993 \cdot 5}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.2.1.3

Multiply.

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Step 3.3.2.1.3.1

Multiply $- 1$ by $- 49958$ .

$y = \frac{49958}{1993 \cdot 5}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 3.3.2.1.3.2

Multiply $1993$ by $5$ .

$y = \frac{49958}{9965}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$y = \frac{49958}{9965}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$y = \frac{49958}{9965}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$y = \frac{49958}{9965}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$y = \frac{49958}{9965}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

$y = \frac{49958}{9965}$

$\frac{126119}{25} - \frac{759 y}{5} = 3700$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4

Replace all occurrences of $y$ with $\frac{49958}{9965}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $\frac{126119}{25} - \frac{759 y}{5} = 3700$ with $\frac{49958}{9965}$ .

$\frac{126119}{25} - \frac{759 (\frac{49958}{9965})}{5} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $\frac{126119}{25} - \frac{759 (\frac{49958}{9965})}{5}$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Combine $759$ and $\frac{49958}{9965}$ .

$\frac{126119}{25} - \frac{\frac{759 \cdot 49958}{9965}}{5} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.1.2

Multiply $759$ by $49958$ .

$\frac{126119}{25} - \frac{\frac{37918122}{9965}}{5} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.1.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{126119}{25} - (\frac{37918122}{9965} \cdot \frac{1}{5}) = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.1.4

Multiply $\frac{37918122}{9965} \cdot \frac{1}{5}$ .

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Step 4.2.1.1.4.1

Multiply $\frac{37918122}{9965}$ by $\frac{1}{5}$ .

$\frac{126119}{25} - \frac{37918122}{9965 \cdot 5} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.1.4.2

Multiply $9965$ by $5$ .

$\frac{126119}{25} - \frac{37918122}{49825} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{126119}{25} - \frac{37918122}{49825} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{126119}{25} - \frac{37918122}{49825} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.2

To write $\frac{126119}{25}$ as a fraction with a common denominator, multiply by $\frac{1993}{1993}$ .

$\frac{126119}{25} \cdot \frac{1993}{1993} - \frac{37918122}{49825} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.3

Write each expression with a common denominator of $49825$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.2.1.3.1

Multiply $\frac{126119}{25}$ by $\frac{1993}{1993}$ .

$\frac{126119 \cdot 1993}{25 \cdot 1993} - \frac{37918122}{49825} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.3.2

Multiply $25$ by $1993$ .

$\frac{126119 \cdot 1993}{49825} - \frac{37918122}{49825} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{126119 \cdot 1993}{49825} - \frac{37918122}{49825} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.4

Combine the numerators over the common denominator.

$\frac{126119 \cdot 1993 - 37918122}{49825} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.5

Simplify the numerator.

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Step 4.2.1.5.1

Multiply $126119$ by $1993$ .

$\frac{251355167 - 37918122}{49825} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.5.2

Subtract $37918122$ from $251355167$ .

$\frac{213437045}{49825} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{213437045}{49825} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.6

Cancel the common factor of $213437045$ and $49825$ .

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Step 4.2.1.6.1

Factor $5$ out of $213437045$ .

$\frac{5 (42687409)}{49825} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.6.2

Cancel the common factors.

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Step 4.2.1.6.2.1

Factor $5$ out of $49825$ .

$\frac{5 \cdot 42687409}{5 \cdot 9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.6.2.2

Cancel the common factor.

$\frac{5 \cdot 42687409}{5 \cdot 9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.2.1.6.2.3

Rewrite the expression.

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{9 y}{5}$

Step 4.3

Replace all occurrences of $y$ in $x = \frac{419}{25} - \frac{9 y}{5}$ with $\frac{49958}{9965}$ .

$x = \frac{419}{25} - \frac{9 (\frac{49958}{9965})}{5}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $\frac{419}{25} - \frac{9 (\frac{49958}{9965})}{5}$ .

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Step 4.4.1.1

Simplify each term.

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Step 4.4.1.1.1

Combine $9$ and $\frac{49958}{9965}$ .

$x = \frac{419}{25} - \frac{\frac{9 \cdot 49958}{9965}}{5}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.1.2

Multiply $9$ by $49958$ .

$x = \frac{419}{25} - \frac{\frac{449622}{9965}}{5}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.1.3

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{419}{25} - (\frac{449622}{9965} \cdot \frac{1}{5})$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.1.4

Multiply $\frac{449622}{9965} \cdot \frac{1}{5}$ .

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Step 4.4.1.1.4.1

Multiply $\frac{449622}{9965}$ by $\frac{1}{5}$ .

$x = \frac{419}{25} - \frac{449622}{9965 \cdot 5}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.1.4.2

Multiply $9965$ by $5$ .

$x = \frac{419}{25} - \frac{449622}{49825}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{449622}{49825}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419}{25} - \frac{449622}{49825}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.2

To write $\frac{419}{25}$ as a fraction with a common denominator, multiply by $\frac{1993}{1993}$ .

$x = \frac{419}{25} \cdot \frac{1993}{1993} - \frac{449622}{49825}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.3

Write each expression with a common denominator of $49825$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.1.3.1

Multiply $\frac{419}{25}$ by $\frac{1993}{1993}$ .

$x = \frac{419 \cdot 1993}{25 \cdot 1993} - \frac{449622}{49825}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.3.2

Multiply $25$ by $1993$ .

$x = \frac{419 \cdot 1993}{49825} - \frac{449622}{49825}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{419 \cdot 1993}{49825} - \frac{449622}{49825}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.4

Combine the numerators over the common denominator.

$x = \frac{419 \cdot 1993 - 449622}{49825}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.5

Simplify the numerator.

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Step 4.4.1.5.1

Multiply $419$ by $1993$ .

$x = \frac{835067 - 449622}{49825}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.5.2

Subtract $449622$ from $835067$ .

$x = \frac{385445}{49825}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{385445}{49825}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.6

Cancel the common factor of $385445$ and $49825$ .

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Step 4.4.1.6.1

Factor $5$ out of $385445$ .

$x = \frac{5 (77089)}{49825}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.6.2

Cancel the common factors.

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Step 4.4.1.6.2.1

Factor $5$ out of $49825$ .

$x = \frac{5 \cdot 77089}{5 \cdot 9965}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.6.2.2

Cancel the common factor.

$x = \frac{5 \cdot 77089}{5 \cdot 9965}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 4.4.1.6.2.3

Rewrite the expression.

$x = \frac{77089}{9965}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{77089}{9965}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{77089}{9965}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{77089}{9965}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{77089}{9965}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

$x = \frac{77089}{9965}$

$\frac{42687409}{9965} = 3700$

$y = \frac{49958}{9965}$

Step 5

Since $\frac{42687409}{9965} = 3700$ is not true, there is no solution.

No solution

Step 6