Solve the System of @WORD x+y>22x-y>1

$x + y > 22 x - y > 1$

Step 1

Solve $x + y > 22 x - y$ for $y$ .

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

Add $y$ to both sides of the inequality.

$x + y + y > 22 x$

Add $y$ and $y$ .

$x + 2 y > 22 x$

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

Subtract $x$ from both sides of the inequality.

$2 y > 22 x - x$

Subtract $x$ from $22 x$ .

$2 y > 21 x$

Divide each term in $2 y > 21 x$ by $2$ and simplify.

Divide each term in $2 y > 21 x$ by $2$ .

$\frac{2 y}{2} > \frac{21 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} > \frac{21 x}{2}$

Divide $y$ by $1$ .

$y > \frac{21 x}{2}$

Step 2

Solve $22 x - y > 1$ for $y$ .

Subtract $22 x$ from both sides of the inequality.

$- y > 1 - 22 x$

Divide each term in $- y > 1 - 22 x$ by $- 1$ and simplify.

Divide each term in $- y > 1 - 22 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} < \frac{1}{- 1} + \frac{- 22 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} < \frac{1}{- 1} + \frac{- 22 x}{- 1}$

Divide $y$ by $1$ .

$y < \frac{1}{- 1} + \frac{- 22 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $1$ by $- 1$ .

$y < - 1 + \frac{- 22 x}{- 1}$

Move the negative one from the denominator of $\frac{- 22 x}{- 1}$ .

$y < - 1 - 1 \cdot (- 22 x)$

Rewrite $- 1 \cdot (- 22 x)$ as $- (- 22 x)$ .

$y < - 1 - (- 22 x)$

Multiply $- 22$ by $- 1$ .

$y < - 1 + 22 x$

Step 3

Find the intersection of $y > \frac{21 x}{2}$ and $y < - 1 + 22 x$ .

$\frac{21 x}{2} < y < - 1 + 22 x$

Step 4

Solve the System of @WORD x+y>22x-y>1

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