Solve the System of Inequalities 6x-y>12 x+5y<-10

$6 x - y > 12$ $x + 5 y < - 10$

Step 1

Solve $6 x - y > 12$ for $y$ .

Subtract $6 x$ from both sides of the inequality.

$- y > 12 - 6 x$

Divide each term in $- y > 12 - 6 x$ by $- 1$ and simplify.

Divide each term in $- y > 12 - 6 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} < \frac{12}{- 1} + \frac{- 6 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} < \frac{12}{- 1} + \frac{- 6 x}{- 1}$

Divide $y$ by $1$ .

$y < \frac{12}{- 1} + \frac{- 6 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 1$ .

$y < - 12 + \frac{- 6 x}{- 1}$

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

$y < - 12 - 1 \cdot (- 6 x)$

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

$y < - 12 - (- 6 x)$

Multiply $- 6$ by $- 1$ .

$y < - 12 + 6 x$

Step 2

Solve $x + 5 y < - 10$ for $y$ .

Subtract $x$ from both sides of the inequality.

$5 y < - 10 - x$

Divide each term in $5 y < - 10 - x$ by $5$ and simplify.

Divide each term in $5 y < - 10 - x$ by $5$ .

$\frac{5 y}{5} < \frac{- 10}{5} + \frac{- x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} < \frac{- 10}{5} + \frac{- x}{5}$

Divide $y$ by $1$ .

$y < \frac{- 10}{5} + \frac{- x}{5}$

Simplify the right side.

Simplify each term.

Divide $- 10$ by $5$ .

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

Move the negative in front of the fraction.

$y < - 2 - \frac{x}{5}$

Step 3

Find the intersection of $y < - 12 + 6 x$ and $y < - 2 - \frac{x}{5}$ .

$y < N o (Min i m u m)$

Step 4

Solve the System of Inequalities 6x-y>12 x+5y<-10

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