Graph the solution set of each given system

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

x < 1
2x + y ≤ 4

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

Graph $x<1$.

$x<1$

Graph $2x+y\le 4$.

Write in $y=mx+b$ form.

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

$y\le 4-2x$

Rearrange terms.

$y\le -2x+4$

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

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

$y=mx+b$

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

$m=-2$

$b=4$

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

Slope: $-2$

$y$-intercept: $\left(0,4\right)$

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

$y\le -2x+4$

Plot each graph on the same coordinate system.

$x<1$

$2x+y\le 4$