Question

solve the system of two linear inequalities graphically.\

$$\begin{cases} y < -5x - 10 \\\\ 4y \\geq 4x + 32 \\end{cases}$$

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

Explanation:

Step1: Simplify the inequality

Divide all terms by 4:
$$\frac{4y}{4} \geq \frac{4x}{4} + \frac{32}{4}$$
Simplify to get: $y \geq x + 8$

Step2: Graph the boundary line

The boundary is $y = x + 8$, a straight line with slope $m=1$ and y-intercept $(0,8)$. Draw it as a solid line (since the inequality is $\geq$, points on the line are included).

Step3: Shade the solution region

Test the origin $(0,0)$: $0 \geq 0 + 8$ is false. Shade the half-plane above the boundary line (all points where $y$ is greater than or equal to $x+8$).

Answer:

1. Draw a solid line for $y = x + 8$ (passing through $(0,8)$ and $(-8,0)$).
2. Shade the area above this solid line. This shaded region represents the solution set of $4y \geq 4x + 32$.