Question

identifying the solution to a system of two - variable inequalities
which equation represents an inequality in the system of inequalities shown in the graph?
$y > 2x + 2$
$y > - 2x - 1$
$y < 2x + 2$
$y < - 2x - 1$
a solution to the system?

Explanation:

Step1: Find dashed line equation

The dashed line has y-intercept $2$ and slope $2$, so its equation is $y=2x+2$. The shaded region is below this dashed line, so the inequality is $y<2x+2$.

Step2: Find solid line equation

The solid line has y-intercept $-1$ and slope $2$, so its equation is $y=2x-1$. The shaded region is above this solid line, so the inequality is $y>2x-1$. Comparing to the options, $y<2x+2$ is provided.

Answer:

$y < 2x + 2$