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

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

Step 1

Solve $x + y < 1 x - y$ for $y$ .

Multiply $x$ by $1$ .

$x + y < x - y$

Move all terms containing $y$ to the left side of the inequality.

Add $y$ to both sides of the inequality.

$x + y + y < x$

Add $y$ and $y$ .

$x + 2 y < x$

Move all terms not containing $y$ to the right side of the inequality.

Subtract $x$ from both sides of the inequality.

$2 y < x - x$

Subtract $x$ from $x$ .

$2 y < 0$

Divide each term in $2 y < 0$ by $2$ and simplify.

Divide each term in $2 y < 0$ by $2$ .

$\frac{2 y}{2} < \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} < \frac{0}{2}$

Divide $y$ by $1$ .

$y < \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$y < 0$

Step 2

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

Multiply $x$ by $1$ .

$x - y > 2$

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 $y < 0$ and $y < - 2 + x$ .

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

Step 4

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

Related Questions

Support LCMGCF.com by disabling your adblocker.