Solve the System of Inequalities 7x-9y<5 -2x+4y>5

$7 x - 9 y < 5$ $- 2 x + 4 y > 5$

Step 1

Solve $7 x - 9 y < 5$ for $y$ .

Subtract $7 x$ from both sides of the inequality.

$- 9 y < 5 - 7 x$

Divide each term in $- 9 y < 5 - 7 x$ by $- 9$ and simplify.

Divide each term in $- 9 y < 5 - 7 x$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 y}{- 9} > \frac{5}{- 9} + \frac{- 7 x}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} > \frac{5}{- 9} + \frac{- 7 x}{- 9}$

Divide $y$ by $1$ .

$y > \frac{5}{- 9} + \frac{- 7 x}{- 9}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y > - \frac{5}{9} + \frac{- 7 x}{- 9}$

Dividing two negative values results in a positive value.

$y > - \frac{5}{9} + \frac{7 x}{9}$

Step 2

Solve $- 2 x + 4 y > 5$ for $y$ .

Add $2 x$ to both sides of the inequality.

$4 y > 5 + 2 x$

Divide each term in $4 y > 5 + 2 x$ by $4$ and simplify.

Divide each term in $4 y > 5 + 2 x$ by $4$ .

$\frac{4 y}{4} > \frac{5}{4} + \frac{2 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} > \frac{5}{4} + \frac{2 x}{4}$

Divide $y$ by $1$ .

$y > \frac{5}{4} + \frac{2 x}{4}$

Simplify the right side.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 x$ .

$y > \frac{5}{4} + \frac{2 (x)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y > \frac{5}{4} + \frac{2 x}{2 \cdot 2}$

Cancel the common factor.

$y > \frac{5}{4} + \frac{2 x}{2 \cdot 2}$

Rewrite the expression.

$y > \frac{5}{4} + \frac{x}{2}$

Step 3

Find the intersection of $y > - \frac{5}{9} + \frac{7 x}{9}$ and $y > \frac{5}{4} + \frac{x}{2}$ .

$y > - \frac{5}{9} + \frac{7 x}{9}$ and $y > \frac{5}{4} + \frac{x}{2}$

Step 4

Solve the System of Inequalities 7x-9y<5 -2x+4y>5

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