Question

solve the system of two linear inequalities graphically.\

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

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

Explanation:

Step1: Identify boundary line

The boundary of $y > x - 2$ 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: Test a point to shade region

Use test point $(0,0)$: $0 > 0 - 2$ → $0 > -2$, which is true. Shade the region above the dashed line.

Answer:

1. Draw a dashed line through the points $(2, 0)$ and $(0, -2)$ (this is $y = x - 2$).
2. Shade the entire region that lies above this dashed line. This shaded area represents the solution set of $y > x - 2$.