Solve the System of Inequalities y<2x+5 4y>-4x-8

$y < 2 x + 5$ $4 y > - 4 x - 8$

Step 1

Divide each term in $4 y > - 4 x - 8$ by $4$ and simplify.

Divide each term in $4 y > - 4 x - 8$ by $4$ .

$\frac{4 y}{4} > \frac{- 4 x}{4} + \frac{- 8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} > \frac{- 4 x}{4} + \frac{- 8}{4}$

Divide $y$ by $1$ .

$y > \frac{- 4 x}{4} + \frac{- 8}{4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 4$ and $4$ .

Factor $4$ out of $- 4 x$ .

$y > \frac{4 (- x)}{4} + \frac{- 8}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$y > \frac{4 (- x)}{4 (1)} + \frac{- 8}{4}$

Cancel the common factor.

$y > \frac{4 (- x)}{4 \cdot 1} + \frac{- 8}{4}$

Rewrite the expression.

$y > \frac{- x}{1} + \frac{- 8}{4}$

Divide $- x$ by $1$ .

$y > - x + \frac{- 8}{4}$

Divide $- 8$ by $4$ .

$y > - x - 2$

Step 2

Find the intersection of $y < 2 x + 5$ and $y > - x - 2$ .

$- x - 2 < y < 2 x + 5$

Step 3