Questions: Lesson: 8.8 Systems of Linear Inequalities Question 3 of 9. Step 1 of 3 y ≤ -6x + 9 y > 2x - 3 Step 1 of 3 : Graph the solution set of the first linear inequality.

Solution Steps

The first inequality is $y \leq -6x + 9$. The boundary line is $y = -6x + 9$. Since the inequality is $\leq$, the line should be solid.

Two points on the line $y = -6x + 9$ are:

• When $x = 0$, $y = -6(0) + 9 = 9$. So, $(0, 9)$ is a point on the line.
• When $x = 1$, $y = -6(1) + 9 = 3$. So, $(1, 3)$ is a point on the line.

Since the inequality is $y \leq -6x + 9$, we shade the region below the line. We can test a point, such as the origin $(0,0)$. Substituting into the inequality: $0 \leq -6(0) + 9$ $0 \leq 9$ which is true. So, the origin is part of the solution set, and we shade below the line.

The second inequality is $y > 2x - 3$. The boundary line is $y = 2x - 3$. Since the inequality is $>$, the line is dashed.

Two points on the line are:

• When $x=0$, $y = 2(0) - 3 = -3$. So, $(0,-3)$ is on the line.
• When $x=1$, $y = 2(1) - 3 = -1$. So, $(1,-1)$ is on the line.

Since the inequality is $y > 2x - 3$, we shade the region above the line. Testing the origin $(0,0)$ gives $0 > 2(0) - 3$, so $0 > -3$ which is true. Thus we shade above the line.

Final Answer