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

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

Solve $x + 3 y < 3$ for $y$ .

Subtract $x$ from both sides of the inequality.

$3 y < 3 - x$

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

Divide each term in $3 y < 3 - x$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $3$ by $3$ .

$y < 1 + \frac{- x}{3}$

Move the negative in front of the fraction.

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

Solve $x - 2 y \geq 4$ for $y$ .

Subtract $x$ from both sides of the inequality.

$- 2 y \geq 4 - x$

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

Divide each term in $- 2 y \geq 4 - x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $4$ by $- 2$ .

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

Dividing two negative values results in a positive value.

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

Find the intersection of $y < 1 - \frac{x}{3}$ and $y \leq - 2 + \frac{x}{2}$ .

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

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

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