Solve the System of Inequalities x+y>2 2x-y>1

$x + y > 2$ $2 x - y > 1$

Subtract $x$ from both sides of the inequality.

$y > 2 - x$

Solve $2 x - y > 1$ for $y$ .

Subtract $2 x$ from both sides of the inequality.

$- y > 1 - 2 x$

Divide each term in $- y > 1 - 2 x$ by $- 1$ and simplify.

Divide each term in $- y > 1 - 2 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} < \frac{1}{- 1} + \frac{- 2 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} < \frac{1}{- 1} + \frac{- 2 x}{- 1}$

Divide $y$ by $1$ .

$y < \frac{1}{- 1} + \frac{- 2 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $1$ by $- 1$ .

$y < - 1 + \frac{- 2 x}{- 1}$

Move the negative one from the denominator of $\frac{- 2 x}{- 1}$ .

$y < - 1 - 1 \cdot (- 2 x)$

Rewrite $- 1 \cdot (- 2 x)$ as $- (- 2 x)$ .

$y < - 1 - (- 2 x)$

Multiply $- 2$ by $- 1$ .

$y < - 1 + 2 x$

Find the intersection of $y > 2 - x$ and $y < - 1 + 2 x$ .

$2 - x < y < - 1 + 2 x$

Solve the System of Inequalities x+y>2 2x-y>1

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