Question

solve the system of two linear inequalities graphically.\

$$\begin{cases} y \\leq -x - 2 \\\\ y > 5x + 10 \\end{cases}$$

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step 1 of 3: graph the solution set of the first linear inequality.

Explanation:

Step1: Identify boundary line

The first inequality is $y \leq -x - 2$. Its boundary is the line $y = -x - 2$. Since the inequality uses $\leq$, the line will be solid (to include points on the line).

Step2: Find intercepts for plotting

• x-intercept: Set $y=0$:

$0 = -x - 2 \implies x = -2$. So the point is $(-2, 0)$.

• y-intercept: Set $x=0$:

$y = -0 - 2 = -2$. So the point is $(0, -2)$.

Step3: Determine shading direction

Choose a test point not on the line, e.g., $(0,0)$:
$0 \leq -0 - 2 \implies 0 \leq -2$, which is false. So shade the half-plane below the solid line $y=-x-2$.

Answer:

Graph the solid line $y = -x - 2$ (passing through $(-2, 0)$ and $(0, -2)$), then shade the region below this line.