Solve the System of Inequalities 2x+4y<=12 3x-y<2

$2 x + 4 y \leq 12$ $3 x - y < 2$

Step 1

Solve $2 x + 4 y \leq 12$ for $y$ .

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

$4 y \leq 12 - 2 x$

Divide each term in $4 y \leq 12 - 2 x$ by $4$ and simplify.

Divide each term in $4 y \leq 12 - 2 x$ by $4$ .

$\frac{4 y}{4} \leq \frac{12}{4} + \frac{- 2 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} \leq \frac{12}{4} + \frac{- 2 x}{4}$

Divide $y$ by $1$ .

$y \leq \frac{12}{4} + \frac{- 2 x}{4}$

Simplify the right side.

Simplify each term.

Divide $12$ by $4$ .

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

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2 x$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

$y \leq 3 + \frac{2 (- x)}{2 (2)}$

Cancel the common factor.

$y \leq 3 + \frac{2 (- x)}{2 \cdot 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 2

Solve $3 x - y < 2$ for $y$ .

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

$- y < 2 - 3 x$

Divide each term in $- y < 2 - 3 x$ by $- 1$ and simplify.

Divide each term in $- y < 2 - 3 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{2}{- 1} + \frac{- 3 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{2}{- 1} + \frac{- 3 x}{- 1}$

Divide $y$ by $1$ .

$y > \frac{2}{- 1} + \frac{- 3 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $2$ by $- 1$ .

$y > - 2 + \frac{- 3 x}{- 1}$

Move the negative one from the denominator of $\frac{- 3 x}{- 1}$ .

$y > - 2 - 1 \cdot (- 3 x)$

Rewrite $- 1 \cdot (- 3 x)$ as $- (- 3 x)$ .

$y > - 2 - (- 3 x)$

Multiply $- 3$ by $- 1$ .

$y > - 2 + 3 x$

Step 3

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

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

Step 4

Solve the System of Inequalities 2x+4y<=12 3x-y<2

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