Question

question
solve the following system of inequalities graphically on the set of axes below. state the coordinates of a point in the solution set.
$y \geq -x + 3$
$y > 2x - 6$

Explanation:

Step1: Graph first inequality boundary

Graph the line $y = -x + 3$. Since the inequality is $y \geq -x + 3$, the line is solid, and we shade the region above the line.

Step2: Graph second inequality boundary

Graph the line $y = 2x - 6$. Since the inequality is $y > 2x - 6$, the line is dashed, and we shade the region above the line.

Step3: Identify overlapping shaded region

The solution set is the area where the two shaded regions overlap.

Step4: Pick a point in overlap

Choose a point that lies within the overlapping shaded area. For example, test $(3, 3)$:

• For $y \geq -x + 3$: $3 \geq -3 + 3 \implies 3 \geq 0$, which is true.
• For $y > 2x - 6$: $3 > 6 - 6 \implies 3 > 0$, which is true.

Answer:

A point in the solution set is $(3, 3)$ (other valid points include $(2, 2)$, $(4, 1)$, etc.)