Graph the solution set of each given system

Missy Lee 2022-03-25 Answered

Graph the solution set of each given system of linear inequalities.

x < 1
2x + y ≤ 4

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Vasquez

Answered 2022-04-28 Author has 460 answers

$x < 1$
$2 x + y \leq 4$

Graph $x < 1$ .

$x < 1$

Graph $2 x + y \leq 4$ .

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

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

$y \leq 4 - 2 x$

Rearrange terms.

$y \leq - 2 x + 4$

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 $y = m x + b$ .

$m = - 2$

$b = 4$

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

Slope: $- 2$

$y$ -intercept: $(0, 4)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- 2 x + 4$ .

$y \leq - 2 x + 4$

Plot each graph on the same coordinate system.

$x < 1$

$2 x + y \leq 4$

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