Graph x+7y<=14 x-2y<=10

$x + 7 y \leq 14$ $x - 2 y \leq 10$

Step 1

Graph $x + 7 y \leq 14$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$7 y \leq 14 - x$

Divide each term in $7 y \leq 14 - x$ by $7$ and simplify.

Divide each term in $7 y \leq 14 - x$ by $7$ .

$\frac{7 y}{7} \leq \frac{14}{7} + \frac{- x}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} \leq \frac{14}{7} + \frac{- x}{7}$

Divide $y$ by $1$ .

$y \leq \frac{14}{7} + \frac{- x}{7}$

Simplify the right side.

Simplify each term.

Divide $14$ by $7$ .

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

Move the negative in front of the fraction.

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

Rearrange terms.

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

Reorder terms.

$y \leq - (\frac{1}{7} x) + 2$

Remove parentheses.

$y \leq - \frac{1}{7} x + 2$

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

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

$m = - \frac{1}{7}$

$b = 2$

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

Slope: $- \frac{1}{7}$

y-intercept: $(0, 2)$

Slope: $- \frac{1}{7}$

y-intercept: $(0, 2)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- \frac{1}{7} x + 2$ .

$y \leq - \frac{1}{7} x + 2$

Step 2

Graph $x - 2 y \leq 10$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$- 2 y \leq 10 - x$

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

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

$\frac{- 2 y}{- 2} \geq \frac{10}{- 2} + \frac{- x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} \geq \frac{10}{- 2} + \frac{- x}{- 2}$

Divide $y$ by $1$ .

$y \geq \frac{10}{- 2} + \frac{- x}{- 2}$

Simplify the right side.

Simplify each term.

Divide $10$ by $- 2$ .

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

Dividing two negative values results in a positive value.

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

Rearrange terms.

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

Reorder terms.

$y \geq \frac{1}{2} x - 5$

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

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

$m = \frac{1}{2}$

$b = - 5$

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

Slope: $\frac{1}{2}$

y-intercept: $(0, - 5)$

Slope: $\frac{1}{2}$

y-intercept: $(0, - 5)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $\frac{1}{2} x - 5$ .

$y \geq \frac{1}{2} x - 5$

Step 3

Plot each graph on the same coordinate system.

$x + 7 y \leq 14$

$x - 2 y \leq 10$

Step 4

Graph x+7y<=14 x-2y<=10

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