Finite Math Examples

$x + y = 15$ , $\frac{10 x + y}{4} + 45 = 10 y + x$

Step 1

Subtract $y$ from both sides of the equation.

$x = 15 - y$

$\frac{10 x + y}{4} + 45 = 10 y + x$

Step 2

Replace all occurrences of $x$ with $15 - y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $\frac{10 x + y}{4} + 45 = 10 y + x$ with $15 - y$ .

$\frac{10 (15 - y) + y}{4} + 45 = 10 y + 15 - y$

$x = 15 - y$

Step 2.2

Simplify $\frac{10 (15 - y) + y}{4} + 45 = 10 y + 15 - y$ .

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Simplify $\frac{10 (15 - y) + y}{4} + 45$ .

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Step 2.2.1.1.1

Remove parentheses.

$\frac{10 (15 - y) + y}{4} + 45 = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.2

Simplify the numerator.

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Step 2.2.1.1.2.1

Apply the distributive property.

$\frac{10 \cdot 15 + 10 (- y) + y}{4} + 45 = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.2.2

Multiply $10$ by $15$ .

$\frac{150 + 10 (- y) + y}{4} + 45 = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.2.3

Multiply $- 1$ by $10$ .

$\frac{150 - 10 y + y}{4} + 45 = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.2.4

Add $- 10 y$ and $y$ .

$\frac{150 - 9 y}{4} + 45 = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.2.5

Factor $3$ out of $150 - 9 y$ .

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Step 2.2.1.1.2.5.1

Factor $3$ out of $150$ .

$\frac{3 (50) - 9 y}{4} + 45 = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.2.5.2

Factor $3$ out of $- 9 y$ .

$\frac{3 (50) + 3 (- 3 y)}{4} + 45 = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.2.5.3

Factor $3$ out of $3 (50) + 3 (- 3 y)$ .

$\frac{3 (50 - 3 y)}{4} + 45 = 10 y + 15 - y$

$x = 15 - y$

$\frac{3 (50 - 3 y)}{4} + 45 = 10 y + 15 - y$

$x = 15 - y$

$\frac{3 (50 - 3 y)}{4} + 45 = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.3

To write $45$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 (50 - 3 y)}{4} + 45 \cdot \frac{4}{4} = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.4

Simplify terms.

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Step 2.2.1.1.4.1

Combine $45$ and $\frac{4}{4}$ .

$\frac{3 (50 - 3 y)}{4} + \frac{45 \cdot 4}{4} = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.4.2

Combine the numerators over the common denominator.

$\frac{3 (50 - 3 y) + 45 \cdot 4}{4} = 10 y + 15 - y$

$x = 15 - y$

$\frac{3 (50 - 3 y) + 45 \cdot 4}{4} = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.5

Simplify the numerator.

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Step 2.2.1.1.5.1

Factor $3$ out of $3 (50 - 3 y) + 45 \cdot 4$ .

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Step 2.2.1.1.5.1.1

Factor $3$ out of $45 \cdot 4$ .

$\frac{3 (50 - 3 y) + 3 (15 \cdot 4)}{4} = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.5.1.2

Factor $3$ out of $3 (50 - 3 y) + 3 (15 \cdot 4)$ .

$\frac{3 (50 - 3 y + 15 \cdot 4)}{4} = 10 y + 15 - y$

$x = 15 - y$

$\frac{3 (50 - 3 y + 15 \cdot 4)}{4} = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.5.2

Multiply $15$ by $4$ .

$\frac{3 (50 - 3 y + 60)}{4} = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.5.3

Add $50$ and $60$ .

$\frac{3 (- 3 y + 110)}{4} = 10 y + 15 - y$

$x = 15 - y$

$\frac{3 (- 3 y + 110)}{4} = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.6

Simplify with factoring out.

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Step 2.2.1.1.6.1

Factor $- 1$ out of $- 3 y$ .

$\frac{3 (- (3 y) + 110)}{4} = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.6.2

Rewrite $110$ as $- 1 (- 110)$ .

$\frac{3 (- (3 y) - 1 \cdot - 110)}{4} = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.6.3

Factor $- 1$ out of $- (3 y) - 1 (- 110)$ .

$\frac{3 (- (3 y - 110))}{4} = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.6.4

Simplify the expression.

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Step 2.2.1.1.6.4.1

Rewrite $- (3 y - 110)$ as $- 1 (3 y - 110)$ .

$\frac{3 (- 1 (3 y - 110))}{4} = 10 y + 15 - y$

$x = 15 - y$

Step 2.2.1.1.6.4.2

Move the negative in front of the fraction.