Precalculus Examples

$12 x - 8 y = - 19$ , $d x + 10 y = - 15$

Step 1

Solve the equation for $x$ .

Tap for more steps...

Step 1.1

Add $8 y$ to both sides of the equation.

$12 x = - 19 + 8 y$

$d x + 10 y = - 15$

Step 1.2

Divide each term in $12 x = - 19 + 8 y$ by $12$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $12 x = - 19 + 8 y$ by $12$ .

$\frac{12 x}{12} = \frac{- 19}{12} + \frac{8 y}{12}$

$d x + 10 y = - 15$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $12$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{- 19}{12} + \frac{8 y}{12}$

$d x + 10 y = - 15$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 19}{12} + \frac{8 y}{12}$

$d x + 10 y = - 15$

$x = \frac{- 19}{12} + \frac{8 y}{12}$

$d x + 10 y = - 15$

$x = \frac{- 19}{12} + \frac{8 y}{12}$

$d x + 10 y = - 15$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Move the negative in front of the fraction.

$x = - \frac{19}{12} + \frac{8 y}{12}$

$d x + 10 y = - 15$

Step 1.2.3.1.2

Cancel the common factor of $8$ and $12$ .

Tap for more steps...

Step 1.2.3.1.2.1

Factor $4$ out of $8 y$ .

$x = - \frac{19}{12} + \frac{4 (2 y)}{12}$

$d x + 10 y = - 15$

Step 1.2.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1.2.2.1

Factor $4$ out of $12$ .

$x = - \frac{19}{12} + \frac{4 (2 y)}{4 (3)}$

$d x + 10 y = - 15$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$x = - \frac{19}{12} + \frac{4 (2 y)}{4 \cdot 3}$

$d x + 10 y = - 15$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$x = - \frac{19}{12} + \frac{2 y}{3}$

$d x + 10 y = - 15$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$d x + 10 y = - 15$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$d x + 10 y = - 15$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$d x + 10 y = - 15$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$d x + 10 y = - 15$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$d x + 10 y = - 15$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$d x + 10 y = - 15$

Step 2

Solve the equation for $y$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$d (- \frac{19}{12}) + d (\frac{2 y}{3}) + 10 y = - 15$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.1.2

Combine $d$ and $\frac{19}{12}$ .

$- \frac{d \cdot 19}{12} + d (\frac{2 y}{3}) + 10 y = - 15$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.1.3

Combine $d$ and $\frac{2 y}{3}$ .

$- \frac{d \cdot 19}{12} + \frac{d (2 y)}{3} + 10 y = - 15$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.1.4

Simplify each term.

Tap for more steps...

Step 2.1.4.1

Move $19$ to the left of $d$ .

$- \frac{19 \cdot d}{12} + \frac{d (2 y)}{3} + 10 y = - 15$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.1.4.2

Move $2$ to the left of $d$ .

$- \frac{19 d}{12} + \frac{2 d y}{3} + 10 y = - 15$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$- \frac{19 d}{12} + \frac{2 d y}{3} + 10 y = - 15$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$- \frac{19 d}{12} + \frac{2 d y}{3} + 10 y = - 15$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.2

Add $\frac{19 d}{12}$ to both sides of the equation.

$\frac{2 d y}{3} + 10 y = - 15 + \frac{19 d}{12}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.3

Factor $2 y$ out of $\frac{2 d y}{3} + 10 y$ .

Tap for more steps...

Step 2.3.1

Factor $2 y$ out of $\frac{2 d y}{3}$ .

$2 y (\frac{d}{3}) + 10 y = - 15 + \frac{19 d}{12}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.3.2

Factor $2 y$ out of $10 y$ .

$2 y (\frac{d}{3}) + 2 y (5) = - 15 + \frac{19 d}{12}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.3.3

Factor $2 y$ out of $2 y \frac{d}{3} + 2 y (5)$ .

$2 y (\frac{d}{3} + 5) = - 15 + \frac{19 d}{12}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$2 y (\frac{d}{3} + 5) = - 15 + \frac{19 d}{12}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4

Divide each term in $2 y (\frac{d}{3} + 5) = - 15 + \frac{19 d}{12}$ by $2 (\frac{d}{3} + 5)$ and simplify.

Tap for more steps...

Step 2.4.1

Divide each term in $2 y (\frac{d}{3} + 5) = - 15 + \frac{19 d}{12}$ by $2 (\frac{d}{3} + 5)$ .

$\frac{2 y (\frac{d}{3} + 5)}{2 (\frac{d}{3} + 5)} = \frac{- 15}{2 (\frac{d}{3} + 5)} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.2

Simplify the left side.

Tap for more steps...

Step 2.4.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.4.2.1.1

Cancel the common factor.

$\frac{2 y (\frac{d}{3} + 5)}{2 (\frac{d}{3} + 5)} = \frac{- 15}{2 (\frac{d}{3} + 5)} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.2.1.2

Rewrite the expression.

$\frac{y (\frac{d}{3} + 5)}{\frac{d}{3} + 5} = \frac{- 15}{2 (\frac{d}{3} + 5)} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$\frac{y (\frac{d}{3} + 5)}{\frac{d}{3} + 5} = \frac{- 15}{2 (\frac{d}{3} + 5)} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.2.2

Cancel the common factor of $\frac{d}{3} + 5$ .

Tap for more steps...

Step 2.4.2.2.1

Cancel the common factor.

$\frac{y (\frac{d}{3} + 5)}{\frac{d}{3} + 5} = \frac{- 15}{2 (\frac{d}{3} + 5)} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.2.2.2

Divide $y$ by $1$ .

$y = \frac{- 15}{2 (\frac{d}{3} + 5)} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$y = \frac{- 15}{2 (\frac{d}{3} + 5)} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$y = \frac{- 15}{2 (\frac{d}{3} + 5)} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3

Simplify the right side.

Tap for more steps...

Step 2.4.3.1

Simplify each term.

Tap for more steps...

Step 2.4.3.1.1

Simplify the denominator.

Tap for more steps...

Step 2.4.3.1.1.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{- 15}{2 (\frac{d}{3} + 5 \cdot \frac{3}{3})} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.1.2

Combine $5$ and $\frac{3}{3}$ .

$y = \frac{- 15}{2 (\frac{d}{3} + \frac{5 \cdot 3}{3})} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.1.3

Combine the numerators over the common denominator.

$y = \frac{- 15}{2 (\frac{d + 5 \cdot 3}{3})} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.1.4

Multiply $5$ by $3$ .

$y = \frac{- 15}{2 (\frac{d + 15}{3})} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$y = \frac{- 15}{2 (\frac{d + 15}{3})} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.2

Combine $2$ and $\frac{d + 15}{3}$ .

$y = \frac{- 15}{\frac{2 (d + 15)}{3}} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.3

Multiply the numerator by the reciprocal of the denominator.

$y = - 15 \frac{3}{2 (d + 15)} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.4

Multiply $- 15 \frac{3}{2 (d + 15)}$ .

Tap for more steps...

Step 2.4.3.1.4.1

Combine $- 15$ and $\frac{3}{2 (d + 15)}$ .

$y = \frac{- 15 \cdot 3}{2 (d + 15)} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.4.2

Multiply $- 15$ by $3$ .

$y = \frac{- 45}{2 (d + 15)} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$y = \frac{- 45}{2 (d + 15)} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.5

Move the negative in front of the fraction.

$y = - \frac{45}{2 (d + 15)} + \frac{\frac{19 d}{12}}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.6

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{12} \cdot \frac{1}{2 (\frac{d}{3} + 5)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.7

Simplify the denominator.

Tap for more steps...

Step 2.4.3.1.7.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{12} \cdot \frac{1}{2 (\frac{d}{3} + 5 \cdot \frac{3}{3})}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.7.2

Combine $5$ and $\frac{3}{3}$ .

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{12} \cdot \frac{1}{2 (\frac{d}{3} + \frac{5 \cdot 3}{3})}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.7.3

Combine the numerators over the common denominator.

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{12} \cdot \frac{1}{2 (\frac{d + 5 \cdot 3}{3})}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.7.4

Multiply $5$ by $3$ .

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{12} \cdot \frac{1}{2 (\frac{d + 15}{3})}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{12} \cdot \frac{1}{2 (\frac{d + 15}{3})}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.8

Combine $2$ and $\frac{d + 15}{3}$ .

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{12} \cdot \frac{1}{\frac{2 (d + 15)}{3}}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.9

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{12} \cdot (1 (\frac{3}{2 (d + 15)}))$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.10

Multiply $\frac{3}{2 (d + 15)}$ by $1$ .

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{12} \cdot \frac{3}{2 (d + 15)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.11

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.4.3.1.11.1

Factor $3$ out of $12$ .

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{3 (4)} \cdot \frac{3}{2 (d + 15)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.11.2

Cancel the common factor.

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{3 \cdot 4} \cdot \frac{3}{2 (d + 15)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.11.3

Rewrite the expression.

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{4} \cdot \frac{1}{2 (d + 15)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{4} \cdot \frac{1}{2 (d + 15)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.12

Multiply $\frac{19 d}{4}$ by $\frac{1}{2 (d + 15)}$ .

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{4 (2 (d + 15))}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 2.4.3.1.13

Multiply $2$ by $4$ .

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = - \frac{19}{12} + \frac{2 y}{3}$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Simplify $- \frac{19}{12} + \frac{2 (- \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)})}{3}$ .

Tap for more steps...

Step 3.1.1

Simplify each term.

Tap for more steps...

Step 3.1.1.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1.1.1

To write $- \frac{45}{2 (d + 15)}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x = - \frac{19}{12} + \frac{2 (- \frac{45}{2 (d + 15)} \cdot \frac{4}{4} + \frac{19 d}{8 (d + 15)})}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.1.1.2

Write each expression with a common denominator of $8 (d + 15)$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1.1.1.2.1

Multiply $\frac{45}{2 (d + 15)}$ by $\frac{4}{4}$ .

$x = - \frac{19}{12} + \frac{2 (- \frac{45 \cdot 4}{2 (d + 15) \cdot 4} + \frac{19 d}{8 (d + 15)})}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.1.1.2.2

Multiply $4$ by $2$ .

$x = - \frac{19}{12} + \frac{2 (- \frac{45 \cdot 4}{8 (d + 15)} + \frac{19 d}{8 (d + 15)})}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = - \frac{19}{12} + \frac{2 (- \frac{45 \cdot 4}{8 (d + 15)} + \frac{19 d}{8 (d + 15)})}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.1.1.3

Combine the numerators over the common denominator.

$x = - \frac{19}{12} + \frac{2 (\frac{- 45 \cdot 4 + 19 d}{8 (d + 15)})}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.1.1.4

Multiply $- 45$ by $4$ .

$x = - \frac{19}{12} + \frac{2 (\frac{- 180 + 19 d}{8 (d + 15)})}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = - \frac{19}{12} + \frac{2 (\frac{- 180 + 19 d}{8 (d + 15)})}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.1.2

Combine $2$ and $\frac{- 180 + 19 d}{8 (d + 15)}$ .

$x = - \frac{19}{12} + \frac{\frac{2 (- 180 + 19 d)}{8 (d + 15)}}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.1.3

Reduce the expression $\frac{2 (- 180 + 19 d)}{8 (d + 15)}$ by cancelling the common factors.

Tap for more steps...

Step 3.1.1.3.1

Factor $2$ out of $8 (d + 15)$ .

$x = - \frac{19}{12} + \frac{\frac{2 (- 180 + 19 d)}{2 (4 (d + 15))}}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.1.3.2

Cancel the common factor.

$x = - \frac{19}{12} + \frac{\frac{2 (- 180 + 19 d)}{2 (4 (d + 15))}}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.1.3.3

Rewrite the expression.

$x = - \frac{19}{12} + \frac{\frac{- 180 + 19 d}{4 (d + 15)}}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = - \frac{19}{12} + \frac{\frac{- 180 + 19 d}{4 (d + 15)}}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.1.4

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{19}{12} + \frac{- 180 + 19 d}{4 (d + 15)} \cdot \frac{1}{3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.1.5

Multiply $\frac{- 180 + 19 d}{4 (d + 15)} \cdot \frac{1}{3}$ .

Tap for more steps...

Step 3.1.1.5.1

Multiply $\frac{- 180 + 19 d}{4 (d + 15)}$ by $\frac{1}{3}$ .

$x = - \frac{19}{12} + \frac{- 180 + 19 d}{4 (d + 15) \cdot 3}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.1.5.2

Multiply $3$ by $4$ .

$x = - \frac{19}{12} + \frac{- 180 + 19 d}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = - \frac{19}{12} + \frac{- 180 + 19 d}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = - \frac{19}{12} + \frac{- 180 + 19 d}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.2

To write $- \frac{19}{12}$ as a fraction with a common denominator, multiply by $\frac{d + 15}{d + 15}$ .

$x = - \frac{19}{12} \cdot \frac{d + 15}{d + 15} + \frac{- 180 + 19 d}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.3

Simplify terms.

Tap for more steps...

Step 3.1.3.1

Multiply $\frac{19}{12}$ by $\frac{d + 15}{d + 15}$ .

$x = - \frac{19 (d + 15)}{12 (d + 15)} + \frac{- 180 + 19 d}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.3.2

Combine the numerators over the common denominator.

$x = \frac{- 19 (d + 15) - 180 + 19 d}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = \frac{- 19 (d + 15) - 180 + 19 d}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.4

Simplify the numerator.

Tap for more steps...

Step 3.1.4.1

Apply the distributive property.

$x = \frac{- 19 d - 19 \cdot 15 - 180 + 19 d}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.4.2

Multiply $- 19$ by $15$ .

$x = \frac{- 19 d - 285 - 180 + 19 d}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.4.3

Add $- 19 d$ and $19 d$ .

$x = \frac{0 - 285 - 180}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.4.4

Subtract $285$ from $0$ .

$x = \frac{- 285 - 180}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.4.5

Subtract $180$ from $- 285$ .

$x = \frac{- 465}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = \frac{- 465}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.5

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1.5.1

Cancel the common factor of $- 465$ and $12$ .

Tap for more steps...

Step 3.1.5.1.1

Factor $3$ out of $- 465$ .

$x = \frac{3 (- 155)}{12 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.5.1.2

Cancel the common factors.

Tap for more steps...

Step 3.1.5.1.2.1

Factor $3$ out of $12 (d + 15)$ .

$x = \frac{3 (- 155)}{3 (4 (d + 15))}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.5.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot - 155}{3 (4 (d + 15))}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.5.1.2.3

Rewrite the expression.

$x = \frac{- 155}{4 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = \frac{- 155}{4 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = \frac{- 155}{4 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

Step 3.1.5.2

Move the negative in front of the fraction.

$x = - \frac{155}{4 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = - \frac{155}{4 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = - \frac{155}{4 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$

$x = - \frac{155}{4 (d + 15)}$

$y = - \frac{45}{2 (d + 15)} + \frac{19 d}{8 (d + 15)}$