Graph 3x+4y>=12 2x-5y>=10

$3 x + 4 y \geq 12$ $2 x - 5 y \geq 10$

Step 1

Graph $3 x + 4 y \geq 12$ .

Write in $y = m x + b$ form.

Solve for $y$ .

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

$4 y \geq 12 - 3 x$

Divide each term in $4 y \geq 12 - 3 x$ by $4$ and simplify.

Divide each term in $4 y \geq 12 - 3 x$ by $4$ .

$\frac{4 y}{4} \geq \frac{12}{4} + \frac{- 3 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} \geq \frac{12}{4} + \frac{- 3 x}{4}$

Divide $y$ by $1$ .

$y \geq \frac{12}{4} + \frac{- 3 x}{4}$

Simplify the right side.

Simplify each term.

Divide $12$ by $4$ .

$y \geq 3 + \frac{- 3 x}{4}$

Move the negative in front of the fraction.

$y \geq 3 - \frac{3 x}{4}$

Rearrange terms.

$y \geq - \frac{3 x}{4} + 3$

Reorder terms.

$y \geq - (\frac{3}{4} x) + 3$

Remove parentheses.

$y \geq - \frac{3}{4} x + 3$

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - \frac{3}{4}$

$b = 3$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- \frac{3}{4}$

y-intercept: $(0, 3)$

Slope: $- \frac{3}{4}$

y-intercept: $(0, 3)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{3}{4} x + 3$ .

$y \geq - \frac{3}{4} x + 3$

Step 2

Graph $2 x - 5 y \geq 10$ .

Write in $y = m x + b$ form.

Solve for $y$ .

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

$- 5 y \geq 10 - 2 x$

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

Divide each term in $- 5 y \geq 10 - 2 x$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $10$ by $- 5$ .

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

Dividing two negative values results in a positive value.

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

Rearrange terms.

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

Reorder terms.

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

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = \frac{2}{5}$

$b = - 2$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{2}{5}$

y-intercept: $(0, - 2)$

Slope: $\frac{2}{5}$

y-intercept: $(0, - 2)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $\frac{2}{5} x - 2$ .

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

Step 3

Plot each graph on the same coordinate system.

$3 x + 4 y \geq 12$

$2 x - 5 y \geq 10$

Step 4

Graph 3x+4y>=12 2x-5y>=10

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