Question

question 2 of 10, step 2 of 3
solve the system of two linear inequalities graphically.
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$$\begin{cases} y \\leq -5x - 10 \\\\ y > x + 2 \\end{cases}$$

step 2 of 3: graph the solution set of the second linear inequality.

Explanation:

Step1: Identify boundary line

The second inequality is $y > x + 2$, so its boundary is the line $y = x + 2$. Since the inequality uses $>$, the line is dashed.

Step2: Find intercepts for plotting

• x-intercept: Set $y=0$, solve $0 = x + 2$ → $x = -2$. So point $(-2, 0)$.
• y-intercept: Set $x=0$, solve $y = 0 + 2$ → $y=2$. So point $(0, 2)$.

Step3: Determine shaded region

Test the origin $(0,0)$: $0 > 0 + 2$ → $0>2$ is false. Shade the region above the dashed line (opposite of the origin side).

Answer:

1. Draw a dashed line through points $(-2, 0)$ and $(0, 2)$ (representing $y = x + 2$).
2. Shade the entire region that lies above this dashed line.