Solve the System of Inequalities -3x-3y>=-18 -x<=-y

$- 3 x - 3 y \geq - 18$ $- x \leq - y$

Step 1

Solve $- 3 x - 3 y \geq - 18$ for $y$ .

Add $3 x$ to both sides of the inequality.

$- 3 y \geq - 18 + 3 x$

Divide each term in $- 3 y \geq - 18 + 3 x$ by $- 3$ and simplify.

Divide each term in $- 3 y \geq - 18 + 3 x$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} \leq \frac{- 18}{- 3} + \frac{3 x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} \leq \frac{- 18}{- 3} + \frac{3 x}{- 3}$

Divide $y$ by $1$ .

$y \leq \frac{- 18}{- 3} + \frac{3 x}{- 3}$

Simplify the right side.

Simplify each term.

Divide $- 18$ by $- 3$ .

$y \leq 6 + \frac{3 x}{- 3}$

Cancel the common factor of $3$ and $- 3$ .

Factor $3$ out of $3 x$ .

$y \leq 6 + \frac{3 (x)}{- 3}$

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

$y \leq 6 - 1 \cdot x$

Rewrite $- 1 \cdot x$ as $- x$ .

$y \leq 6 - x$

Step 2

Solve $- x \leq - y$ for $y$ .

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

$- y \geq - x$

Divide each term in $- y \geq - x$ by $- 1$ and simplify.

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

$y \leq x$

Step 3

Find the intersection of $y \leq 6 - x$ and $y \leq x$ .

$y \leq N o (Min i m u m)$

Step 4

Solve the System of Inequalities -3x-3y>=-18 -x<=-y

Related Questions

Support LCMGCF.com by disabling your adblocker.