Find the Intersection y<=-2x+5 y>=3x+3

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

Simplify the first inequality.

Rewrite so $x$ is on the left side of the inequality.

$- 2 x + 5 \geq y$

Subtract $5$ from both sides of the inequality.

$- 2 x \geq y - 5$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

Simplify the second inequality.

Rewrite so $x$ is on the left side of the inequality.

$3 x + 3 \leq y$

Subtract $3$ from both sides of the inequality.

$3 x \leq y - 3$

Divide each term in $3 x \leq y - 3$ by $3$ and simplify.

Divide each term in $3 x \leq y - 3$ by $3$ .

$\frac{3 x}{3} \leq \frac{y}{3} + \frac{- 3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{y}{3} + \frac{- 3}{3}$

Divide $x$ by $1$ .

$x \leq \frac{y}{3} + \frac{- 3}{3}$

Simplify the right side.

Divide $- 3$ by $3$ .

$x \leq \frac{y}{3} - 1$

Find the Intersection y<=-2x+5 y>=3x+3

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