Question

solve the system of two linear inequalities graphically.\

$$\begin{cases}2y < -x + 2 \\\\ 2y \\geq 6x - 12\\end{cases}$$

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step 1 of 3 : graph the solution set of the first linear inequality.

Explanation:

Step1: Isolate y for first inequality

Rearrange to solve for y:
$\frac{2y}{2} < \frac{-x + 2}{2}$
$y < -\frac{1}{2}x + 1$

Step2: Identify boundary line

The boundary is $y = -\frac{1}{2}x + 1$, drawn as a dashed line (since the inequality is $<$).

Step3: Test a point for shading

Use (0,0): $0 < -\frac{1}{2}(0) + 1$ → $0 < 1$, which is true. Shade the region below the dashed line.

Answer:

Graph the dashed line $y = -\frac{1}{2}x + 1$, then shade all points below this line to represent the solution set of $2y < -x + 2$.