Question

solve the system of two linear inequalities graphically.\

$$\begin{cases}-3y < -4x + 18\\\\-3y \\geq 6x - 27\\end{cases}$$

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

Explanation:

Step1: Isolate y in the inequality

Divide all terms by -3, reverse inequality sign:
$$-3y \geq 6x - 27$$
$$y \leq -2x + 9$$

Step2: Identify boundary line

The boundary is $y = -2x + 9$, solid line (due to $\leq$).

Step3: Test a reference point

Use (0,0): $0 \leq -2(0) + 9$ → $0 \leq 9$, true. Shade the region containing (0,0) (below the line).

Answer:

1. Graph the solid line $y = -2x + 9$ (this line has a y-intercept at (0,9) and a slope of -2, so it also passes through (4.5, 0)).
2. Shade the entire region below and including this solid line (since the test point (0,0) satisfies the inequality, this is the valid solution set for the second inequality).