Solve by Graphing y=-1/4x-2 , 3x-4y=24

$y = - \frac{1}{4} x - 2$ , $3 x - 4 y = 24$

Step 1

Combine $x$ and $\frac{1}{4}$ .

$y = - \frac{x}{4} - 2$

$3 x - 4 y = 24$

Step 2

Subtract $3 x$ from both sides of the equation.

$- 4 y = 24 - 3 x$

$y = - \frac{x}{4} - 2$

Step 3

Divide each term in $- 4 y = 24 - 3 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 24 - 3 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{24}{- 4} + \frac{- 3 x}{- 4}$

$y = - \frac{x}{4} - 2$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{24}{- 4} + \frac{- 3 x}{- 4}$

$y = - \frac{x}{4} - 2$

Divide $y$ by $1$ .

$y = \frac{24}{- 4} + \frac{- 3 x}{- 4}$

$y = - \frac{x}{4} - 2$

$y = \frac{24}{- 4} + \frac{- 3 x}{- 4}$

$y = - \frac{x}{4} - 2$

$y = \frac{24}{- 4} + \frac{- 3 x}{- 4}$

$y = - \frac{x}{4} - 2$

Simplify the right side.

Simplify each term.

Divide $24$ by $- 4$ .

$y = - 6 + \frac{- 3 x}{- 4}$

$y = - \frac{x}{4} - 2$

Dividing two negative values results in a positive value.

$y = - 6 + \frac{3 x}{4}$

$y = - \frac{x}{4} - 2$

$y = - 6 + \frac{3 x}{4}$

$y = - \frac{x}{4} - 2$

$y = - 6 + \frac{3 x}{4}$

$y = - \frac{x}{4} - 2$

$y = - 6 + \frac{3 x}{4}$

$y = - \frac{x}{4} - 2$

Step 4

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

$(4, - 3)$

Step 5