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 3 of 3 : graph the solution set for the system.

Explanation:

Step1: Simplify first inequality

Divide by -3, reverse inequality:
$$-3y < -4x + 18 \implies y > \frac{4}{3}x - 6$$
This is a dashed line with slope $\frac{4}{3}$, y-intercept $-6$; shade above the line.

Step2: Simplify second inequality

Divide by -3, reverse inequality:
$$-3y \geq 6x - 27 \implies y \leq -2x + 9$$
This is a solid line with slope $-2$, y-intercept $9$; shade below the line.

Step3: Identify solution region

The solution set is the overlapping shaded area: above the dashed line $y=\frac{4}{3}x - 6$ and below the solid line $y=-2x + 9$.

Answer:

The solution set is the region that lies above the dashed line $y=\frac{4}{3}x - 6$ and below the solid line $y=-2x + 9$ (the overlapping shaded area of the two inequalities).