Solve the System of @WORD 2x+4y<=123x-y<2

$2 x + 4 y \leq 123 x - y < 2$

Step 1

Solve $2 x + 4 y \leq 123 x - y$ for $y$ .

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

Add $y$ to both sides of the inequality.

$2 x + 4 y + y \leq 123 x$

Add $4 y$ and $y$ .

$2 x + 5 y \leq 123 x$

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

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

$5 y \leq 123 x - 2 x$

Subtract $2 x$ from $123 x$ .

$5 y \leq 121 x$

Divide each term in $5 y \leq 121 x$ by $5$ and simplify.

Divide each term in $5 y \leq 121 x$ by $5$ .

$\frac{5 y}{5} \leq \frac{121 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} \leq \frac{121 x}{5}$

Divide $y$ by $1$ .

$y \leq \frac{121 x}{5}$

Step 2

Solve $123 x - y < 2$ for $y$ .

Subtract $123 x$ from both sides of the inequality.

$- y < 2 - 123 x$

Divide each term in $- y < 2 - 123 x$ by $- 1$ and simplify.

Divide each term in $- y < 2 - 123 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{2}{- 1} + \frac{- 123 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{2}{- 1} + \frac{- 123 x}{- 1}$

Divide $y$ by $1$ .

$y > \frac{2}{- 1} + \frac{- 123 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $2$ by $- 1$ .

$y > - 2 + \frac{- 123 x}{- 1}$

Move the negative one from the denominator of $\frac{- 123 x}{- 1}$ .

$y > - 2 - 1 \cdot (- 123 x)$

Rewrite $- 1 \cdot (- 123 x)$ as $- (- 123 x)$ .

$y > - 2 - (- 123 x)$

Multiply $- 123$ by $- 1$ .

$y > - 2 + 123 x$

Step 3

Find the intersection of $y \leq \frac{121 x}{5}$ and $y > - 2 + 123 x$ .

$- 2 + 123 x < y \leq \frac{121 x}{5}$

Step 4

Solve the System of @WORD 2x+4y<=123x-y<2

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