Solve the System of @WORD x+2y>=103x-4y>12

$x + 2 y \geq 103 x - 4 y > 12$

Step 1

Solve $x + 2 y \geq 103 x - 4 y$ for $y$ .

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

Add $4 y$ to both sides of the inequality.

$x + 2 y + 4 y \geq 103 x$

Add $2 y$ and $4 y$ .

$x + 6 y \geq 103 x$

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

Subtract $x$ from both sides of the inequality.

$6 y \geq 103 x - x$

Subtract $x$ from $103 x$ .

$6 y \geq 102 x$

Divide each term in $6 y \geq 102 x$ by $6$ and simplify.

Divide each term in $6 y \geq 102 x$ by $6$ .

$\frac{6 y}{6} \geq \frac{102 x}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} \geq \frac{102 x}{6}$

Divide $y$ by $1$ .

$y \geq \frac{102 x}{6}$

Simplify the right side.

Cancel the common factor of $102$ and $6$ .

Factor $6$ out of $102 x$ .

$y \geq \frac{6 (17 x)}{6}$

Cancel the common factors.

Factor $6$ out of $6$ .

$y \geq \frac{6 (17 x)}{6 (1)}$

Cancel the common factor.

$y \geq \frac{6 (17 x)}{6 \cdot 1}$

Rewrite the expression.

$y \geq \frac{17 x}{1}$

Divide $17 x$ by $1$ .

$y \geq 17 x$

Step 2

Solve $103 x - 4 y > 12$ for $y$ .

Subtract $103 x$ from both sides of the inequality.

$- 4 y > 12 - 103 x$

Divide each term in $- 4 y > 12 - 103 x$ by $- 4$ and simplify.

Divide each term in $- 4 y > 12 - 103 x$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} < \frac{12}{- 4} + \frac{- 103 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} < \frac{12}{- 4} + \frac{- 103 x}{- 4}$

Divide $y$ by $1$ .

$y < \frac{12}{- 4} + \frac{- 103 x}{- 4}$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 4$ .

$y < - 3 + \frac{- 103 x}{- 4}$

Dividing two negative values results in a positive value.

$y < - 3 + \frac{103 x}{4}$

Step 3

Find the intersection of $y \geq 17 x$ and $y < - 3 + \frac{103 x}{4}$ .

$17 x \leq y < - 3 + \frac{103 x}{4}$

Step 4

Solve the System of @WORD x+2y>=103x-4y>12

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