Solve the System of Inequalities x-4y>=6 3x+2y>5

$x - 4 y \geq 6$ $3 x + 2 y > 5$

Step 1

Solve $x - 4 y \geq 6$ for $y$ .

Subtract $x$ from both sides of the inequality.

$- 4 y \geq 6 - x$

Divide each term in $- 4 y \geq 6 - x$ by $- 4$ and simplify.

Divide each term in $- 4 y \geq 6 - x$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} \leq \frac{6}{- 4} + \frac{- x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} \leq \frac{6}{- 4} + \frac{- x}{- 4}$

Divide $y$ by $1$ .

$y \leq \frac{6}{- 4} + \frac{- x}{- 4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $6$ and $- 4$ .

Factor $2$ out of $6$ .

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

Cancel the common factors.

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

Step 2

Solve $3 x + 2 y > 5$ for $y$ .

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

$2 y > 5 - 3 x$

Divide each term in $2 y > 5 - 3 x$ by $2$ and simplify.

Divide each term in $2 y > 5 - 3 x$ by $2$ .

$\frac{2 y}{2} > \frac{5}{2} + \frac{- 3 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} > \frac{5}{2} + \frac{- 3 x}{2}$

Divide $y$ by $1$ .

$y > \frac{5}{2} + \frac{- 3 x}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$y > \frac{5}{2} - \frac{3 x}{2}$

Step 3

Find the intersection of $y \leq - \frac{3}{2} + \frac{x}{4}$ and $y > \frac{5}{2} - \frac{3 x}{2}$ .

$\frac{5}{2} - \frac{3 x}{2} < y \leq - \frac{3}{2} + \frac{x}{4}$

Step 4

Solve the System of Inequalities x-4y>=6 3x+2y>5

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