Questions: Question 5 of 10 On a piece of paper, graph this system of inequalities. Then determine which region contains the solution to the system. y <= -(1/3) x+3 y >= 3 x+2 Text description for graph A. Region B B. Region A

Question 5 of 10

On a piece of paper, graph this system of inequalities. Then determine which region contains the solution to the system.

y <= -(1/3) x+3
y >= 3 x+2

Text description for graph
A. Region B
B. Region A

Transcript text: 5.4.3 Quiz: Two-Variable Systems of Inequalities Question 5 of 10 On a piece of paper, graph this system of inequalities. Then determine which region contains the solution to the system. \[ \begin{array}{l} y \leq-\frac{1}{3} x+3 \\ y \geq 3 x+2 \end{array} \] Text description for graph A. Region B B. Region $A$

Solution

Solution Steps

Step 1: Find the solution region for the first inequality

The first inequality is _y_ ≤ (-1/3)_x_ + 3. The corresponding line is _y_ = (-1/3)_x_ + 3, which has a _y_-intercept of 3 and a slope of -1/3. Since the inequality is less than or equal to, we shade the region below the line.

Step 2: Find the solution region for the second inequality

The second inequality is _y_ ≥ 3_x_ + 2. The corresponding line is _y_ = 3_x_ + 2, which has a _y_-intercept of 2 and a slope of 3. Since the inequality is greater than or equal to, we shade the region above the line.

Step 3: Find the intersection of the regions

The solution to the system of inequalities is the region where the shaded areas from both inequalities overlap. On the graph, this is Region A.