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

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

Step 1

Solve $2 x - y > 5$ for $y$ .

Subtract $2 x$ from both sides of the inequality.

$- y > 5 - 2 x$

Divide each term in $- y > 5 - 2 x$ by $- 1$ and simplify.

Divide each term in $- y > 5 - 2 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} < \frac{5}{- 1} + \frac{- 2 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} < \frac{5}{- 1} + \frac{- 2 x}{- 1}$

Divide $y$ by $1$ .

$y < \frac{5}{- 1} + \frac{- 2 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $5$ by $- 1$ .

$y < - 5 + \frac{- 2 x}{- 1}$

Move the negative one from the denominator of $\frac{- 2 x}{- 1}$ .

$y < - 5 - 1 \cdot (- 2 x)$

Rewrite $- 1 \cdot (- 2 x)$ as $- (- 2 x)$ .

$y < - 5 - (- 2 x)$

Multiply $- 2$ by $- 1$ .

$y < - 5 + 2 x$

Step 2

Solve $2 y + x > 8$ for $y$ .

Subtract $x$ from both sides of the inequality.

$2 y > 8 - x$

Divide each term in $2 y > 8 - x$ by $2$ and simplify.

Divide each term in $2 y > 8 - x$ by $2$ .

$\frac{2 y}{2} > \frac{8}{2} + \frac{- x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} > \frac{8}{2} + \frac{- x}{2}$

Divide $y$ by $1$ .

$y > \frac{8}{2} + \frac{- x}{2}$

Simplify the right side.

Simplify each term.

Divide $8$ by $2$ .

$y > 4 + \frac{- x}{2}$

Move the negative in front of the fraction.

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

Step 3

Find the intersection of $y < - 5 + 2 x$ and $y > 4 - \frac{x}{2}$ .

$4 - \frac{x}{2} < y < - 5 + 2 x$

Step 4

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

Related Questions

Support LCMGCF.com by disabling your adblocker.