Question

solve the system of two linear inequalities graphically.\

$$\begin{cases}-2y < -3x - 12\\\\-y \\geq 2x + 4\\end{cases}$$

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

Explanation:

Step1: Rearrange inequality to solve for y

Multiply both sides by -1 (reverse inequality sign):
$$y \leq -2x - 4$$

Step2: Identify boundary line

The boundary is the line $y = -2x - 4$. Since the inequality is $\leq$, the line is solid.

Step3: Test a point to find solution region

Test $(0,0)$: $0 \leq -2(0) - 4$ → $0 \leq -4$, which is false. So the solution region is below/on the boundary line.

Answer:

1. First, draw the solid boundary line $y = -2x - 4$ (this line has a y-intercept at $(0, -4)$ and a slope of $-2$).
2. Shade the region below and including this solid line to represent the solution set of $-y \geq 2x + 4$ (or $y \leq -2x - 4$).