Finite Math Examples

$- 8 x - 3 y = 18$ , $22 x + 38 y = 248$ , $15 x + 10 y = 10$

Step 1

Solve for $x$ in $- 8 x - 3 y = 18$ .

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Step 1.1

Add $3 y$ to both sides of the equation.

$- 8 x = 18 + 3 y$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

Step 1.2

Divide each term in $- 8 x = 18 + 3 y$ by $- 8$ and simplify.

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Step 1.2.1

Divide each term in $- 8 x = 18 + 3 y$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{18}{- 8} + \frac{3 y}{- 8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 8$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{18}{- 8} + \frac{3 y}{- 8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{18}{- 8} + \frac{3 y}{- 8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

$x = \frac{18}{- 8} + \frac{3 y}{- 8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

$x = \frac{18}{- 8} + \frac{3 y}{- 8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

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 $18$ and $- 8$ .

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Step 1.2.3.1.1.1

Factor $2$ out of $18$ .

$x = \frac{2 (9)}{- 8} + \frac{3 y}{- 8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $2$ out of $- 8$ .

$x = \frac{2 \cdot 9}{2 \cdot - 4} + \frac{3 y}{- 8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 9}{2 \cdot - 4} + \frac{3 y}{- 8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$x = \frac{9}{- 4} + \frac{3 y}{- 8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

$x = \frac{9}{- 4} + \frac{3 y}{- 8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

$x = \frac{9}{- 4} + \frac{3 y}{- 8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$x = - \frac{9}{4} + \frac{3 y}{- 8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$x = - \frac{9}{4} - \frac{3 y}{8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$22 x + 38 y = 248$

$15 x + 10 y = 10$

Step 2

Replace all occurrences of $x$ with $- \frac{9}{4} - \frac{3 y}{8}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $22 x + 38 y = 248$ with $- \frac{9}{4} - \frac{3 y}{8}$ .

$22 (- \frac{9}{4} - \frac{3 y}{8}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $22 (- \frac{9}{4} - \frac{3 y}{8}) + 38 y$ .

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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.

$22 (- \frac{9}{4}) + 22 (- \frac{3 y}{8}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Move the leading negative in $- \frac{9}{4}$ into the numerator.

$22 (\frac{- 9}{4}) + 22 (- \frac{3 y}{8}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.2.2

Factor $2$ out of $22$ .

$2 (11) (\frac{- 9}{4}) + 22 (- \frac{3 y}{8}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.2.3

Factor $2$ out of $4$ .

$2 \cdot (11 (\frac{- 9}{2 \cdot 2})) + 22 (- \frac{3 y}{8}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.2.4

Cancel the common factor.

$2 \cdot (11 (\frac{- 9}{2 \cdot 2})) + 22 (- \frac{3 y}{8}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.2.5

Rewrite the expression.

$11 (\frac{- 9}{2}) + 22 (- \frac{3 y}{8}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

$11 (\frac{- 9}{2}) + 22 (- \frac{3 y}{8}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.3

Combine $11$ and $\frac{- 9}{2}$ .

$\frac{11 \cdot - 9}{2} + 22 (- \frac{3 y}{8}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.4

Multiply $11$ by $- 9$ .

$\frac{- 99}{2} + 22 (- \frac{3 y}{8}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.5

Cancel the common factor of $2$ .

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Step 2.2.1.1.5.1

Move the leading negative in $- \frac{3 y}{8}$ into the numerator.

$\frac{- 99}{2} + 22 (\frac{- 3 y}{8}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.5.2

Factor $2$ out of $22$ .

$\frac{- 99}{2} + 2 (11) (\frac{- 3 y}{8}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.5.3

Factor $2$ out of $8$ .

$\frac{- 99}{2} + 2 \cdot (11 (\frac{- 3 y}{2 \cdot 4})) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.5.4

Cancel the common factor.

$\frac{- 99}{2} + 2 \cdot (11 (\frac{- 3 y}{2 \cdot 4})) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.5.5

Rewrite the expression.

$\frac{- 99}{2} + 11 (\frac{- 3 y}{4}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

$\frac{- 99}{2} + 11 (\frac{- 3 y}{4}) + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.6

Combine $11$ and $\frac{- 3 y}{4}$ .

$\frac{- 99}{2} + \frac{11 (- 3 y)}{4} + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.7

Multiply $- 3$ by $11$ .

$\frac{- 99}{2} + \frac{- 33 y}{4} + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.8

Simplify each term.

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Step 2.2.1.1.8.1

Move the negative in front of the fraction.

$- \frac{99}{2} + \frac{- 33 y}{4} + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.1.8.2

Move the negative in front of the fraction.

$- \frac{99}{2} - \frac{33 y}{4} + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

$- \frac{99}{2} - \frac{33 y}{4} + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

$- \frac{99}{2} - \frac{33 y}{4} + 38 y = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.2

To write $38 y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{99}{2} - \frac{33 y}{4} + 38 y \cdot \frac{4}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.3

Simplify terms.

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Step 2.2.1.3.1

Combine $38 y$ and $\frac{4}{4}$ .

$- \frac{99}{2} - \frac{33 y}{4} + \frac{38 y \cdot 4}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.3.2

Combine the numerators over the common denominator.

$- \frac{99}{2} + \frac{- 33 y + 38 y \cdot 4}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

$- \frac{99}{2} + \frac{- 33 y + 38 y \cdot 4}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

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 $y$ out of $- 33 y + 38 y \cdot 4$ .

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Step 2.2.1.4.1.1.1

Factor $y$ out of $- 33 y$ .

$- \frac{99}{2} + \frac{y \cdot - 33 + 38 y \cdot 4}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.4.1.1.2

Factor $y$ out of $38 y \cdot 4$ .

$- \frac{99}{2} + \frac{y \cdot - 33 + y (38 \cdot 4)}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.4.1.1.3

Factor $y$ out of $y \cdot - 33 + y (38 \cdot 4)$ .

$- \frac{99}{2} + \frac{y (- 33 + 38 \cdot 4)}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

$- \frac{99}{2} + \frac{y (- 33 + 38 \cdot 4)}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.4.1.2

Multiply $38$ by $4$ .

$- \frac{99}{2} + \frac{y (- 33 + 152)}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.4.1.3

Add $- 33$ and $152$ .

$- \frac{99}{2} + \frac{y \cdot 119}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

$- \frac{99}{2} + \frac{y \cdot 119}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.2.1.4.2

Move $119$ to the left of $y$ .

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$15 x + 10 y = 10$

Step 2.3

Replace all occurrences of $x$ in $15 x + 10 y = 10$ with $- \frac{9}{4} - \frac{3 y}{8}$ .

$15 (- \frac{9}{4} - \frac{3 y}{8}) + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $15 (- \frac{9}{4} - \frac{3 y}{8}) + 10 y$ .

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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.

$15 (- \frac{9}{4}) + 15 (- \frac{3 y}{8}) + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.1.2

Multiply $15 (- \frac{9}{4})$ .

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Step 2.4.1.1.2.1

Multiply $- 1$ by $15$ .

$- 15 (\frac{9}{4}) + 15 (- \frac{3 y}{8}) + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.1.2.2

Combine $- 15$ and $\frac{9}{4}$ .

$\frac{- 15 \cdot 9}{4} + 15 (- \frac{3 y}{8}) + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.1.2.3

Multiply $- 15$ by $9$ .

$\frac{- 135}{4} + 15 (- \frac{3 y}{8}) + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$\frac{- 135}{4} + 15 (- \frac{3 y}{8}) + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.1.3

Multiply $15 (- \frac{3 y}{8})$ .

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Step 2.4.1.1.3.1

Multiply $- 1$ by $15$ .

$\frac{- 135}{4} - 15 \frac{3 y}{8} + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.1.3.2

Combine $- 15$ and $\frac{3 y}{8}$ .

$\frac{- 135}{4} + \frac{- 15 (3 y)}{8} + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.1.3.3

Multiply $3$ by $- 15$ .

$\frac{- 135}{4} + \frac{- 45 y}{8} + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$\frac{- 135}{4} + \frac{- 45 y}{8} + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.1.4

Simplify each term.

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Step 2.4.1.1.4.1

Move the negative in front of the fraction.

$- \frac{135}{4} + \frac{- 45 y}{8} + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.1.4.2

Move the negative in front of the fraction.

$- \frac{135}{4} - \frac{45 y}{8} + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$- \frac{135}{4} - \frac{45 y}{8} + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$- \frac{135}{4} - \frac{45 y}{8} + 10 y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.2

To write $10 y$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{135}{4} - \frac{45 y}{8} + 10 y \cdot \frac{8}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.3

Simplify terms.

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Step 2.4.1.3.1

Combine $10 y$ and $\frac{8}{8}$ .

$- \frac{135}{4} - \frac{45 y}{8} + \frac{10 y \cdot 8}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.3.2

Combine the numerators over the common denominator.

$- \frac{135}{4} + \frac{- 45 y + 10 y \cdot 8}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$- \frac{135}{4} + \frac{- 45 y + 10 y \cdot 8}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.4

Simplify the numerator.

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Step 2.4.1.4.1

Factor $5 y$ out of $- 45 y + 10 y \cdot 8$ .

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Step 2.4.1.4.1.1

Factor $5 y$ out of $- 45 y$ .

$- \frac{135}{4} + \frac{5 y (- 9) + 10 y \cdot 8}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.4.1.2

Factor $5 y$ out of $10 y \cdot 8$ .

$- \frac{135}{4} + \frac{5 y (- 9) + 5 y (2 \cdot 8)}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.4.1.3

Factor $5 y$ out of $5 y (- 9) + 5 y (2 \cdot 8)$ .

$- \frac{135}{4} + \frac{5 y (- 9 + 2 \cdot 8)}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$- \frac{135}{4} + \frac{5 y (- 9 + 2 \cdot 8)}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.4.2

Multiply $2$ by $8$ .

$- \frac{135}{4} + \frac{5 y (- 9 + 16)}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.4.3

Add $- 9$ and $16$ .

$- \frac{135}{4} + \frac{5 y \cdot 7}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 2.4.1.4.4

Multiply $7$ by $5$ .

$- \frac{135}{4} + \frac{35 y}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$- \frac{135}{4} + \frac{35 y}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$- \frac{135}{4} + \frac{35 y}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$- \frac{135}{4} + \frac{35 y}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$- \frac{135}{4} + \frac{35 y}{8} = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3

Solve for $y$ in $- \frac{135}{4} + \frac{35 y}{8} = 10$ .

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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

Add $\frac{135}{4}$ to both sides of the equation.

$\frac{35 y}{8} = 10 + \frac{135}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.1.2

To write $10$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{35 y}{8} = 10 \cdot \frac{4}{4} + \frac{135}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.1.3

Combine $10$ and $\frac{4}{4}$ .

$\frac{35 y}{8} = \frac{10 \cdot 4}{4} + \frac{135}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{35 y}{8} = \frac{10 \cdot 4 + 135}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Multiply $10$ by $4$ .

$\frac{35 y}{8} = \frac{40 + 135}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.1.5.2

Add $40$ and $135$ .

$\frac{35 y}{8} = \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$\frac{35 y}{8} = \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$\frac{35 y}{8} = \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.2

Multiply both sides of the equation by $\frac{8}{35}$ .

$\frac{8}{35} \cdot \frac{35 y}{8} = \frac{8}{35} \cdot \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

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 $\frac{8}{35} \cdot \frac{35 y}{8}$ .

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Step 3.3.1.1.1

Cancel the common factor of $8$ .

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Step 3.3.1.1.1.1

Cancel the common factor.

$\frac{8}{35} \cdot \frac{35 y}{8} = \frac{8}{35} \cdot \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.3.1.1.1.2

Rewrite the expression.

$\frac{1}{35} \cdot (35 y) = \frac{8}{35} \cdot \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$\frac{1}{35} \cdot (35 y) = \frac{8}{35} \cdot \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.3.1.1.2

Cancel the common factor of $35$ .

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Step 3.3.1.1.2.1

Factor $35$ out of $35 y$ .

$\frac{1}{35} \cdot (35 (y)) = \frac{8}{35} \cdot \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{1}{35} \cdot (35 y) = \frac{8}{35} \cdot \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.3.1.1.2.3

Rewrite the expression.

$y = \frac{8}{35} \cdot \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$y = \frac{8}{35} \cdot \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$y = \frac{8}{35} \cdot \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$y = \frac{8}{35} \cdot \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $\frac{8}{35} \cdot \frac{175}{4}$ .

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Step 3.3.2.1.1

Cancel the common factor of $4$ .

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Step 3.3.2.1.1.1

Factor $4$ out of $8$ .

$y = \frac{4 (2)}{35} \cdot \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.3.2.1.1.2

Cancel the common factor.

$y = \frac{4 \cdot 2}{35} \cdot \frac{175}{4}$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.3.2.1.1.3

Rewrite the expression.

$y = \frac{2}{35} \cdot 175$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$y = \frac{2}{35} \cdot 175$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.3.2.1.2

Cancel the common factor of $35$ .

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Step 3.3.2.1.2.1

Factor $35$ out of $175$ .

$y = \frac{2}{35} \cdot (35 (5))$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.3.2.1.2.2

Cancel the common factor.

$y = \frac{2}{35} \cdot (35 \cdot 5)$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.3.2.1.2.3

Rewrite the expression.

$y = 2 \cdot 5$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$y = 2 \cdot 5$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 3.3.2.1.3

Multiply $2$ by $5$ .

$y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$y = 10$

$- \frac{99}{2} + \frac{119 y}{4} = 248$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 4

Replace all occurrences of $y$ with $10$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $- \frac{99}{2} + \frac{119 y}{4} = 248$ with $10$ .

$- \frac{99}{2} + \frac{119 (10)}{4} = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $- \frac{99}{2} + \frac{119 (10)}{4}$ .

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Step 4.2.1.1

Multiply $119$ by $10$ .

$- \frac{99}{2} + \frac{1190}{4} = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 4.2.1.2

Cancel the common factor of $1190$ and $4$ .

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Step 4.2.1.2.1

Factor $2$ out of $1190$ .

$- \frac{99}{2} + \frac{2 (595)}{4} = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 4.2.1.2.2

Cancel the common factors.

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Step 4.2.1.2.2.1

Factor $2$ out of $4$ .

$- \frac{99}{2} + \frac{2 \cdot 595}{2 \cdot 2} = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 4.2.1.2.2.2

Cancel the common factor.

$- \frac{99}{2} + \frac{2 \cdot 595}{2 \cdot 2} = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 4.2.1.2.2.3

Rewrite the expression.

$- \frac{99}{2} + \frac{595}{2} = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$- \frac{99}{2} + \frac{595}{2} = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$- \frac{99}{2} + \frac{595}{2} = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 4.2.1.3

Combine the numerators over the common denominator.

$\frac{- 99 + 595}{2} = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 4.2.1.4

Simplify the expression.

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Step 4.2.1.4.1

Add $- 99$ and $595$ .

$\frac{496}{2} = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 4.2.1.4.2

Divide $496$ by $2$ .

$248 = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$248 = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$248 = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

$248 = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 y}{8}$

Step 4.3

Replace all occurrences of $y$ in $x = - \frac{9}{4} - \frac{3 y}{8}$ with $10$ .

$x = - \frac{9}{4} - \frac{3 (10)}{8}$

$248 = 248$

$y = 10$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $- \frac{9}{4} - \frac{3 (10)}{8}$ .

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Step 4.4.1.1

Simplify each term.

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Step 4.4.1.1.1

Cancel the common factor of $10$ and $8$ .

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Step 4.4.1.1.1.1

Factor $2$ out of $3 (10)$ .

$x = - \frac{9}{4} - \frac{2 (3 \cdot (5))}{8}$

$248 = 248$

$y = 10$

Step 4.4.1.1.1.2

Cancel the common factors.

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Step 4.4.1.1.1.2.1

Factor $2$ out of $8$ .

$x = - \frac{9}{4} - \frac{2 (3 \cdot (5))}{2 (4)}$

$248 = 248$

$y = 10$

Step 4.4.1.1.1.2.2

Cancel the common factor.

$x = - \frac{9}{4} - \frac{2 (3 \cdot (5))}{2 \cdot 4}$

$248 = 248$

$y = 10$

Step 4.4.1.1.1.2.3

Rewrite the expression.

$x = - \frac{9}{4} - \frac{3 \cdot (5)}{4}$

$248 = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 \cdot (5)}{4}$

$248 = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{3 \cdot (5)}{4}$

$248 = 248$

$y = 10$

Step 4.4.1.1.2

Multiply $3$ by $5$ .

$x = - \frac{9}{4} - \frac{15}{4}$

$248 = 248$

$y = 10$

$x = - \frac{9}{4} - \frac{15}{4}$

$248 = 248$

$y = 10$

Step 4.4.1.2

Combine fractions.

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Step 4.4.1.2.1

Combine the numerators over the common denominator.

$x = \frac{- 9 - 15}{4}$

$248 = 248$

$y = 10$

Step 4.4.1.2.2

Simplify the expression.

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Step 4.4.1.2.2.1

Subtract $15$ from $- 9$ .

$x = \frac{- 24}{4}$

$248 = 248$

$y = 10$

Step 4.4.1.2.2.2

Divide $- 24$ by $4$ .

$x = - 6$

$248 = 248$

$y = 10$

$x = - 6$

$248 = 248$

$y = 10$

$x = - 6$

$248 = 248$

$y = 10$

$x = - 6$

$248 = 248$

$y = 10$

$x = - 6$

$248 = 248$

$y = 10$

$x = - 6$

$248 = 248$

$y = 10$

Step 5

Remove any equations from the system that are always true.

$x = - 6$

$y = 10$

Step 6

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 6, 10)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 6, 10)$

Equation Form:

$x = - 6, y = 10$

Step 8