Solve by Graphing 12x-5y=30 y=2x-6

$12 x - 5 y = 30$ $y = 2 x - 6$

Step 1

Subtract $12 x$ from both sides of the equation.

$- 5 y = 30 - 12 x$

$y = 2 x - 6$

Step 2

Divide each term in $- 5 y = 30 - 12 x$ by $- 5$ and simplify.

Divide each term in $- 5 y = 30 - 12 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{30}{- 5} + \frac{- 12 x}{- 5}$

$y = 2 x - 6$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{30}{- 5} + \frac{- 12 x}{- 5}$

$y = 2 x - 6$

Divide $y$ by $1$ .

$y = \frac{30}{- 5} + \frac{- 12 x}{- 5}$

$y = 2 x - 6$

$y = \frac{30}{- 5} + \frac{- 12 x}{- 5}$

$y = 2 x - 6$

$y = \frac{30}{- 5} + \frac{- 12 x}{- 5}$

$y = 2 x - 6$

Simplify the right side.

Simplify each term.

Divide $30$ by $- 5$ .

$y = - 6 + \frac{- 12 x}{- 5}$

$y = 2 x - 6$

Dividing two negative values results in a positive value.

$y = - 6 + \frac{12 x}{5}$

$y = 2 x - 6$

$y = - 6 + \frac{12 x}{5}$

$y = 2 x - 6$

$y = - 6 + \frac{12 x}{5}$

$y = 2 x - 6$

$y = - 6 + \frac{12 x}{5}$

$y = 2 x - 6$

Step 3

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(0, - 6)$

Step 4