Graph x+y<3 -5x+2y<=10

$x + y < 3$ $- 5 x + 2 y \leq 10$

Step 1

Graph $x + y < 3$ .

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

Subtract $x$ from both sides of the inequality.

$y < 3 - x$

Rearrange terms.

$y < - x + 3$

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

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

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

$m = - 1$

$b = 3$

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

Slope: $- 1$

y-intercept: $(0, 3)$

Slope: $- 1$

y-intercept: $(0, 3)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- x + 3$ .

$y < - x + 3$

Step 2

Graph $- 5 x + 2 y \leq 10$ .

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

Solve for $y$ .

Add $5 x$ to both sides of the inequality.

$2 y \leq 10 + 5 x$

Divide each term in $2 y \leq 10 + 5 x$ by $2$ and simplify.

Divide each term in $2 y \leq 10 + 5 x$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $10$ by $2$ .

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

Rearrange terms.

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

Reorder terms.

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

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

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

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

$b = 5$

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: $(0, 5)$

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

y-intercept: $(0, 5)$

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

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

Step 3

Plot each graph on the same coordinate system.

$x + y < 3$

$- 5 x + 2 y \leq 10$

Step 4

Graph x+y<3 -5x+2y<=10

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