Solve the System of @WORD x+y<1 , x-y>2

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

Step 1

Subtract $x$ from both sides of the inequality.

$y < 1 - x$

Step 2

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

Subtract $x$ from both sides of the inequality.

$- y > 2 - x$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $2$ by $- 1$ .

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

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

$y < - 2 + x$

Step 3

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

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

Step 4

Solve the System of @WORD x+y<1 , x-y>2

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