Question

11 multiple choice 4 points match the system with the given graph. x + 2y ≥ -2 y ≤ 2 2x - y ≤ -2 y ≤ 2 x - 2y ≤ 1 0x + y ≤ 2 x + 2y ≥ 2 x + 0y ≤ 2 12 multiple choice 4 points solve: -3 < -x < 9 -3 < x < 9 9 < x < -3 3 < x < -9 -9 < x < 3

Explanation:

11.

Step1: Analyze the horizontal - line

The horizontal line in the graph is \(y = 2\) and the region below it is shaded, so one of the inequalities is \(y\leq2\).

Step2: Analyze the slanted - line

For the line \(x + 2y=-2\), rewrite it in slope - intercept form \(y=-\frac{1}{2}x - 1\). The region above this line is shaded, so the inequality is \(x + 2y\geq - 2\).

Step1: Multiply the inequality by - 1

When we multiply the compound inequality \(-3 < -x<9\) by \(- 1\), we need to reverse the inequality signs according to the rule that if \(a < b\), then \(-a>-b\) when multiplying by a negative number.
\((-1)\times(-3)>(-1)\times(-x)>(-1)\times9\)

Step2: Simplify the inequality

We get \(3 > x>-9\), which can be written as \(-9 < x<3\).

Answer:

\(x + 2y\geq - 2,y\leq2\)

12.