Solve the System of @WORD 3x+y>=-3x+2y<=4

$3 x + y \geq - 3 x + 2 y \leq 4$

Step 1

Solve $3 x + y \geq - 3 x + 2 y$ for $y$ .

Move all terms containing $y$ to the left side of the inequality.

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

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

Subtract $2 y$ from $y$ .

$3 x - y \geq - 3 x$

Move all terms not containing $y$ to the right side of the inequality.

Subtract $3 x$ from both sides of the inequality.

$- y \geq - 3 x - 3 x$

Subtract $3 x$ from $- 3 x$ .

$- y \geq - 6 x$

Divide each term in $- y \geq - 6 x$ by $- 1$ and simplify.

Divide each term in $- y \geq - 6 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} \leq \frac{- 6 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} \leq \frac{- 6 x}{- 1}$

Divide $y$ by $1$ .

$y \leq \frac{- 6 x}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{- 6 x}{- 1}$ .

$y \leq - 1 \cdot (- 6 x)$

Rewrite $- 1 \cdot (- 6 x)$ as $- (- 6 x)$ .

$y \leq - (- 6 x)$

Multiply $- 6$ by $- 1$ .

$y \leq 6 x$

Step 2

Solve $- 3 x + 2 y \leq 4$ for $y$ .

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

$2 y \leq 4 + 3 x$

Divide each term in $2 y \leq 4 + 3 x$ by $2$ and simplify.

Divide each term in $2 y \leq 4 + 3 x$ by $2$ .

$\frac{2 y}{2} \leq \frac{4}{2} + \frac{3 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} \leq \frac{4}{2} + \frac{3 x}{2}$

Divide $y$ by $1$ .

$y \leq \frac{4}{2} + \frac{3 x}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$y \leq 2 + \frac{3 x}{2}$

Step 3

Find the intersection of $y \leq 6 x$ and $y \leq 2 + \frac{3 x}{2}$ .

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

Step 4

Solve the System of @WORD 3x+y>=-3x+2y<=4

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