Question

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

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

Explanation:

Step1: Identify boundary line

The boundary line is $y=5x+10$. Since the inequality is $y>5x+10$, the line is dashed (not included in the solution).

Step2: Find intercepts for plotting

• x-intercept: Set $y=0$, solve $0=5x+10$

$\implies 5x=-10 \implies x=-2$. So point $(-2, 0)$.

• y-intercept: Set $x=0$, solve $y=5(0)+10$

$\implies y=10$. So point $(0, 10)$.

Step3: Determine shading region

Test a point not on the line, e.g., $(0,0)$:
$0 > 5(0)+10 \implies 0>10$, which is false. Shade the region above the dashed line (opposite of the test point).

Answer:

1. Draw a dashed line through points $(-2, 0)$ and $(0, 10)$ (this is $y=5x+10$).
2. Shade the area that lies strictly above this dashed line.