Solve by Graphing 4x-5y=0 , 8x-10y=15

$4 x - 5 y = 0$ , $8 x - 10 y = 15$

Step 1

Subtract $4 x$ from both sides of the equation.

$- 5 y = - 4 x$

$8 x - 10 y = 15$

Step 2

Divide each term in $- 5 y = - 4 x$ by $- 5$ and simplify.

Divide each term in $- 5 y = - 4 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- 4 x}{- 5}$

$8 x - 10 y = 15$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{- 4 x}{- 5}$

$8 x - 10 y = 15$

Divide $y$ by $1$ .

$y = \frac{- 4 x}{- 5}$

$8 x - 10 y = 15$

$y = \frac{- 4 x}{- 5}$

$8 x - 10 y = 15$

$y = \frac{- 4 x}{- 5}$

$8 x - 10 y = 15$

Simplify the right side.

Dividing two negative values results in a positive value.

$y = \frac{4 x}{5}$

$8 x - 10 y = 15$

$y = \frac{4 x}{5}$

$8 x - 10 y = 15$

$y = \frac{4 x}{5}$

$8 x - 10 y = 15$

Step 3

Subtract $8 x$ from both sides of the equation.

$- 10 y = 15 - 8 x$

$y = \frac{4 x}{5}$

Step 4

Divide each term in $- 10 y = 15 - 8 x$ by $- 10$ and simplify.

Divide each term in $- 10 y = 15 - 8 x$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{15}{- 10} + \frac{- 8 x}{- 10}$

$y = \frac{4 x}{5}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{15}{- 10} + \frac{- 8 x}{- 10}$

$y = \frac{4 x}{5}$

Divide $y$ by $1$ .

$y = \frac{15}{- 10} + \frac{- 8 x}{- 10}$

$y = \frac{4 x}{5}$

$y = \frac{15}{- 10} + \frac{- 8 x}{- 10}$

$y = \frac{4 x}{5}$

$y = \frac{15}{- 10} + \frac{- 8 x}{- 10}$

$y = \frac{4 x}{5}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $15$ and $- 10$ .

Factor $5$ out of $15$ .

$y = \frac{5 (3)}{- 10} + \frac{- 8 x}{- 10}$

$y = \frac{4 x}{5}$

Cancel the common factors.

Factor $5$ out of $- 10$ .

$y = \frac{5 \cdot 3}{5 \cdot - 2} + \frac{- 8 x}{- 10}$

$y = \frac{4 x}{5}$

Cancel the common factor.

$y = \frac{5 \cdot 3}{5 \cdot - 2} + \frac{- 8 x}{- 10}$

$y = \frac{4 x}{5}$

Rewrite the expression.

$y = \frac{3}{- 2} + \frac{- 8 x}{- 10}$

$y = \frac{4 x}{5}$

$y = \frac{3}{- 2} + \frac{- 8 x}{- 10}$

$y = \frac{4 x}{5}$

$y = \frac{3}{- 2} + \frac{- 8 x}{- 10}$

$y = \frac{4 x}{5}$

Move the negative in front of the fraction.

$y = - \frac{3}{2} + \frac{- 8 x}{- 10}$

$y = \frac{4 x}{5}$

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

Factor $- 2$ out of $- 8 x$ .

$y = - \frac{3}{2} + \frac{- 2 (4 x)}{- 10}$

$y = \frac{4 x}{5}$

Cancel the common factors.

Factor $- 2$ out of $- 10$ .

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

$y = \frac{4 x}{5}$

Cancel the common factor.

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

$y = \frac{4 x}{5}$

Rewrite the expression.