Solve the System of Inequalities 2x+5y<10 3x-4y>=-8

$2 x + 5 y < 10$ $3 x - 4 y \geq - 8$

Step 1

Solve $2 x + 5 y < 10$ for $y$ .

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

$5 y < 10 - 2 x$

Divide each term in $5 y < 10 - 2 x$ by $5$ and simplify.

Divide each term in $5 y < 10 - 2 x$ by $5$ .

$\frac{5 y}{5} < \frac{10}{5} + \frac{- 2 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} < \frac{10}{5} + \frac{- 2 x}{5}$

Divide $y$ by $1$ .

$y < \frac{10}{5} + \frac{- 2 x}{5}$

Simplify the right side.

Simplify each term.

Divide $10$ by $5$ .

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

Move the negative in front of the fraction.

$y < 2 - \frac{2 x}{5}$

Step 2

Solve $3 x - 4 y \geq - 8$ for $y$ .

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

$- 4 y \geq - 8 - 3 x$

Divide each term in $- 4 y \geq - 8 - 3 x$ by $- 4$ and simplify.

Divide each term in $- 4 y \geq - 8 - 3 x$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} \leq \frac{- 8}{- 4} + \frac{- 3 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} \leq \frac{- 8}{- 4} + \frac{- 3 x}{- 4}$

Divide $y$ by $1$ .

$y \leq \frac{- 8}{- 4} + \frac{- 3 x}{- 4}$

Simplify the right side.

Simplify each term.

Divide $- 8$ by $- 4$ .

$y \leq 2 + \frac{- 3 x}{- 4}$

Dividing two negative values results in a positive value.

$y \leq 2 + \frac{3 x}{4}$

Step 3

Find the intersection of $y < 2 - \frac{2 x}{5}$ and $y \leq 2 + \frac{3 x}{4}$ .

$y \leq N o (Min i m u m)$

Step 4

Solve the System of Inequalities 2x+5y<10 3x-4y>=-8

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