Solve by Graphing y=-1/2x-4 , 5x-2y=20

$y = - \frac{1}{2} x - 4$ , $5 x - 2 y = 20$

Step 1

Combine $x$ and $\frac{1}{2}$ .

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

$5 x - 2 y = 20$

Step 2

Subtract $5 x$ from both sides of the equation.

$- 2 y = 20 - 5 x$

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

Step 3

Divide each term in $- 2 y = 20 - 5 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 20 - 5 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{20}{- 2} + \frac{- 5 x}{- 2}$

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{20}{- 2} + \frac{- 5 x}{- 2}$

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

Divide $y$ by $1$ .

$y = \frac{20}{- 2} + \frac{- 5 x}{- 2}$

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

$y = \frac{20}{- 2} + \frac{- 5 x}{- 2}$

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

$y = \frac{20}{- 2} + \frac{- 5 x}{- 2}$

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

Simplify the right side.

Simplify each term.

Divide $20$ by $- 2$ .

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

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

Dividing two negative values results in a positive value.

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

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

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

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

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

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

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

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

Step 4

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

$(2, - 5)$

Step 5