Find the Intersection -2x+3y>=1 -5x+6y<=1

$- 2 x + 3 y \geq 1$ $- 5 x + 6 y \leq 1$

Step 1

Simplify the first inequality.

Subtract $3 y$ from both sides of the inequality.

$- 2 x \geq 1 - 3 y$

Divide each term in $- 2 x \geq 1 - 3 y$ by $- 2$ and simplify.

Divide each term in $- 2 x \geq 1 - 3 y$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \leq \frac{1}{- 2} + \frac{- 3 y}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \leq \frac{1}{- 2} + \frac{- 3 y}{- 2}$

Divide $x$ by $1$ .

$x \leq \frac{1}{- 2} + \frac{- 3 y}{- 2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x \leq - \frac{1}{2} + \frac{- 3 y}{- 2}$

Dividing two negative values results in a positive value.

$x \leq - \frac{1}{2} + \frac{3 y}{2}$

Step 2

Simplify the second inequality.

Subtract $6 y$ from both sides of the inequality.

$- 5 x \leq 1 - 6 y$

Divide each term in $- 5 x \leq 1 - 6 y$ by $- 5$ and simplify.

Divide each term in $- 5 x \leq 1 - 6 y$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \geq \frac{1}{- 5} + \frac{- 6 y}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} \geq \frac{1}{- 5} + \frac{- 6 y}{- 5}$

Divide $x$ by $1$ .

$x \geq \frac{1}{- 5} + \frac{- 6 y}{- 5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x \geq - \frac{1}{5} + \frac{- 6 y}{- 5}$

Dividing two negative values results in a positive value.

$x \geq - \frac{1}{5} + \frac{6 y}{5}$

Step 3

Find the Intersection -2x+3y>=1 -5x+6y<=1

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