Algebra Examples

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

Step 1

Graph $x + 3 y < - 18$ .

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Solve for $y$ .

Tap for more steps...

Step 1.1.1.1

Subtract $x$ from both sides of the inequality.

$3 y < - 18 - x$

Step 1.1.1.2

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

Tap for more steps...

Step 1.1.1.2.1

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

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

Step 1.1.1.2.2

Simplify the left side.

Tap for more steps...

Step 1.1.1.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.1.1.2.2.1.1

Cancel the common factor.

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

Step 1.1.1.2.2.1.2

Divide $y$ by $1$ .

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

Step 1.1.1.2.3

Simplify the right side.

Tap for more steps...

Step 1.1.1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.1.1.2.3.1.1

Divide $- 18$ by $3$ .

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

Step 1.1.1.2.3.1.2

Move the negative in front of the fraction.

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

Step 1.1.2

Rearrange terms.

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

Step 1.1.3

Reorder terms.

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

Step 1.1.4

Remove parentheses.

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

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

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

$b = - 6$

Step 1.2.2

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: $(0, - 6)$

Step 1.3

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 $5 x + 2 y \leq 14$ .

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

Solve for $y$ .

Tap for more steps...

Step 2.1.1.1

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

$2 y \leq 14 - 5 x$

Step 2.1.1.2

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

Tap for more steps...

Step 2.1.1.2.1

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

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

Step 2.1.1.2.2

Simplify the left side.

Tap for more steps...

Step 2.1.1.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.2.2.1.1

Cancel the common factor.

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

Step 2.1.1.2.2.1.2

Divide $y$ by $1$ .

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

Step 2.1.1.2.3

Simplify the right side.

Tap for more steps...

Step 2.1.1.2.3.1

Simplify each term.

Tap for more steps...

Step 2.1.1.2.3.1.1

Divide $14$ by $2$ .

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

Step 2.1.1.2.3.1.2

Move the negative in front of the fraction.

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

Step 2.1.2

Rearrange terms.

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

Step 2.1.3

Reorder terms.

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

Step 2.1.4

Remove parentheses.

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

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

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

$b = 7$

Step 2.2.2

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: $(0, 7)$

Step 2.3

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