Solve the System of Inequalities x>2 5x-2y>6

$x > 2$ $5 x - 2 y > 6$

Solve $5 x - 2 y > 6$ for $y$ .

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

$- 2 y > 6 - 5 x$

Divide each term in $- 2 y > 6 - 5 x$ by $- 2$ and simplify.

Divide each term in $- 2 y > 6 - 5 x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} < \frac{6}{- 2} + \frac{- 5 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} < \frac{6}{- 2} + \frac{- 5 x}{- 2}$

Divide $y$ by $1$ .

$y < \frac{6}{- 2} + \frac{- 5 x}{- 2}$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 2$ .

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

Dividing two negative values results in a positive value.

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

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

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

Solve the System of Inequalities x>2 5x-2y>6

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