Solve the System of Inequalities 5x-6y>42 3x+2y<=14

$5 x - 6 y > 42$ $3 x + 2 y \leq 14$

Step 1

Solve $5 x - 6 y > 42$ for $y$ .

Subtract $5 x$ from both sides of the inequality.

$- 6 y > 42 - 5 x$

Divide each term in $- 6 y > 42 - 5 x$ by $- 6$ and simplify.

Divide each term in $- 6 y > 42 - 5 x$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 y}{- 6} < \frac{42}{- 6} + \frac{- 5 x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} < \frac{42}{- 6} + \frac{- 5 x}{- 6}$

Divide $y$ by $1$ .

$y < \frac{42}{- 6} + \frac{- 5 x}{- 6}$

Simplify the right side.

Simplify each term.

Divide $42$ by $- 6$ .

$y < - 7 + \frac{- 5 x}{- 6}$

Dividing two negative values results in a positive value.

$y < - 7 + \frac{5 x}{6}$

Step 2

Solve $3 x + 2 y \leq 14$ for $y$ .

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

$2 y \leq 14 - 3 x$

Divide each term in $2 y \leq 14 - 3 x$ by $2$ and simplify.

Divide each term in $2 y \leq 14 - 3 x$ by $2$ .

$\frac{2 y}{2} \leq \frac{14}{2} + \frac{- 3 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} \leq \frac{14}{2} + \frac{- 3 x}{2}$

Divide $y$ by $1$ .

$y \leq \frac{14}{2} + \frac{- 3 x}{2}$

Simplify the right side.

Simplify each term.

Divide $14$ by $2$ .

$y \leq 7 + \frac{- 3 x}{2}$

Move the negative in front of the fraction.

$y \leq 7 - \frac{3 x}{2}$

Step 3

Find the intersection of $y < - 7 + \frac{5 x}{6}$ and $y \leq 7 - \frac{3 x}{2}$ .

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

Step 4

Solve the System of Inequalities 5x-6y>42 3x+2y<=14

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