Solve the System of Inequalities 5x+2y>19 x+y>=5

$5 x + 2 y > 19$ $x + y \geq 5$

Step 1

Solve $5 x + 2 y > 19$ for $y$ .

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

$2 y > 19 - 5 x$

Divide each term in $2 y > 19 - 5 x$ by $2$ and simplify.

Divide each term in $2 y > 19 - 5 x$ by $2$ .

$\frac{2 y}{2} > \frac{19}{2} + \frac{- 5 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} > \frac{19}{2} + \frac{- 5 x}{2}$

Divide $y$ by $1$ .

$y > \frac{19}{2} + \frac{- 5 x}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$y > \frac{19}{2} - \frac{5 x}{2}$

Step 2

Subtract $x$ from both sides of the inequality.

$y \geq 5 - x$

Step 3

Find the intersection of $y > \frac{19}{2} - \frac{5 x}{2}$ and $y \geq 5 - x$ .

$y > \frac{19}{2} - \frac{5 x}{2}$ and $y \geq 5 - x$

Step 4