Solve the System of Inequalities -7x+3y>-1 5x-9y>-6

$- 7 x + 3 y > - 1$ $5 x - 9 y > - 6$

Step 1

Solve $- 7 x + 3 y > - 1$ for $y$ .

Add $7 x$ to both sides of the inequality.

$3 y > - 1 + 7 x$

Divide each term in $3 y > - 1 + 7 x$ by $3$ and simplify.

Divide each term in $3 y > - 1 + 7 x$ by $3$ .

$\frac{3 y}{3} > \frac{- 1}{3} + \frac{7 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} > \frac{- 1}{3} + \frac{7 x}{3}$

Divide $y$ by $1$ .

$y > \frac{- 1}{3} + \frac{7 x}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$y > - \frac{1}{3} + \frac{7 x}{3}$

Step 2

Solve $5 x - 9 y > - 6$ for $y$ .

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

$- 9 y > - 6 - 5 x$

Divide each term in $- 9 y > - 6 - 5 x$ by $- 9$ and simplify.

Divide each term in $- 9 y > - 6 - 5 x$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 y}{- 9} < \frac{- 6}{- 9} + \frac{- 5 x}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} < \frac{- 6}{- 9} + \frac{- 5 x}{- 9}$

Divide $y$ by $1$ .

$y < \frac{- 6}{- 9} + \frac{- 5 x}{- 9}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 6$ and $- 9$ .

Factor $- 3$ out of $- 6$ .

$y < \frac{- 3 (2)}{- 9} + \frac{- 5 x}{- 9}$

Cancel the common factors.

Factor $- 3$ out of $- 9$ .

$y < \frac{- 3 \cdot 2}{- 3 \cdot 3} + \frac{- 5 x}{- 9}$

Cancel the common factor.

$y < \frac{- 3 \cdot 2}{- 3 \cdot 3} + \frac{- 5 x}{- 9}$

Rewrite the expression.

$y < \frac{2}{3} + \frac{- 5 x}{- 9}$

Dividing two negative values results in a positive value.

$y < \frac{2}{3} + \frac{5 x}{9}$

Step 3

Find the intersection of $y > - \frac{1}{3} + \frac{7 x}{3}$ and $y < \frac{2}{3} + \frac{5 x}{9}$ .

$- \frac{1}{3} + \frac{7 x}{3} < y < \frac{2}{3} + \frac{5 x}{9}$

Step 4

Solve the System of Inequalities -7x+3y>-1 5x-9y>-6

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