Solve the System of Inequalities x+y>=3 x+2y>=5

$x + y \geq 3$ $x + 2 y \geq 5$

Step 1

Subtract $x$ from both sides of the inequality.

$y \geq 3 - x$

Step 2

Solve $x + 2 y \geq 5$ for $y$ .

Subtract $x$ from both sides of the inequality.

$2 y \geq 5 - x$

Divide each term in $2 y \geq 5 - x$ by $2$ and simplify.

Divide each term in $2 y \geq 5 - x$ by $2$ .

$\frac{2 y}{2} \geq \frac{5}{2} + \frac{- x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} \geq \frac{5}{2} + \frac{- x}{2}$

Divide $y$ by $1$ .

$y \geq \frac{5}{2} + \frac{- x}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$y \geq \frac{5}{2} - \frac{x}{2}$

Step 3

Find the intersection of $y \geq 3 - x$ and $y \geq \frac{5}{2} - \frac{x}{2}$ .

$y \geq 3 - x$ and $y \geq \frac{5}{2} - \frac{x}{2}$

Step 4