Question

use system of inequalities to answer questionspart a which graph best represent the system of inequalitiespart b find two solutions for the system of inequalities and verify algebraically

Answer 1

For part A, u

se the equation of the line to graph each inequality

$y=x-2$

Graph the function and shade the region that is more than the line

Graph the second line

$y=-\frac{2}{3}x+1$

Now mix this graphs

The correct answer is a

For part B, we only need to chose 2 points that belong to the shaded region, they could be

A (-3,2) and B (-4,-1)

Now verify this algebraically

For Point A:

$\begin{gathered} y\ge x-2 \\ 2\ge-3-2 \\ 2\ge-5 \\ y\leq-\frac{2}{3}x+1 \\ 2\leq-\frac{2}{3}\cdot(-3)+1 \\ 2\leq2+1 \\ 2\leq3 \end{gathered}$

For point B

$\begin{gathered} y\ge x-2 \\ -1\ge-4-2 \\ -1\ge-6 \\ y\leq-\frac{2}{3}x+1 \\ -1\leq-\frac{2}{3}\cdot(-4)+1 \\ -1\leq\frac{8}{3}+1 \\ -1\leq\frac{11}{3} \end{gathered}$