Graph x+3y<-18 5x+2y<=14

$x + 3 y < - 18$ $5 x + 2 y \leq 14$

Step 1

Graph $x + 3 y < - 18$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$3 y < - 18 - x$

Divide each term in $3 y < - 18 - x$ by $3$ and simplify.

Divide each term in $3 y < - 18 - x$ by $3$ .

$\frac{3 y}{3} < \frac{- 18}{3} + \frac{- x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} < \frac{- 18}{3} + \frac{- x}{3}$

Divide $y$ by $1$ .

$y < \frac{- 18}{3} + \frac{- x}{3}$

Simplify the right side.

Simplify each term.

Divide $- 18$ by $3$ .

$y < - 6 + \frac{- x}{3}$

Move the negative in front of the fraction.

$y < - 6 - \frac{x}{3}$

Rearrange terms.

$y < - \frac{x}{3} - 6$

Reorder terms.

$y < - (\frac{1}{3} x) - 6$

Remove parentheses.

$y < - \frac{1}{3} x - 6$

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

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

$m = - \frac{1}{3}$

$b = - 6$

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

Slope: $- \frac{1}{3}$

y-intercept: $(0, - 6)$

Slope: $- \frac{1}{3}$

y-intercept: $(0, - 6)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{1}{3} x - 6$ .

$y < - \frac{1}{3} x - 6$

Step 2

Graph $5 x + 2 y \leq 14$ .

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

Solve for $y$ .

Subtract $5 x$ from both sides of the inequality.

$2 y \leq 14 - 5 x$

Divide each term in $2 y \leq 14 - 5 x$ by $2$ and simplify.

Divide each term in $2 y \leq 14 - 5 x$ by $2$ .

$\frac{2 y}{2} \leq \frac{14}{2} + \frac{- 5 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} \leq \frac{14}{2} + \frac{- 5 x}{2}$

Divide $y$ by $1$ .

$y \leq \frac{14}{2} + \frac{- 5 x}{2}$

Simplify the right side.

Simplify each term.

Divide $14$ by $2$ .

$y \leq 7 + \frac{- 5 x}{2}$

Move the negative in front of the fraction.

$y \leq 7 - \frac{5 x}{2}$

Rearrange terms.

$y \leq - \frac{5 x}{2} + 7$

Reorder terms.

$y \leq - (\frac{5}{2} x) + 7$

Remove parentheses.

$y \leq - \frac{5}{2} x + 7$

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

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

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

$b = 7$

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

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

y-intercept: $(0, 7)$

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

y-intercept: $(0, 7)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- \frac{5}{2} x + 7$ .

$y \leq - \frac{5}{2} x + 7$

Step 3

Plot each graph on the same coordinate system.

$x + 3 y < - 18$

$5 x + 2 y \leq 14$

Step 4

Graph x+3y<-18 5x+2y<=14

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