Question

graph the solution of the system of linear inequalities. x - y ≥ 6 x + y ≤ 2 use the graphing tool to graph the system of inequalities. click to enlarge graph

Explanation:

Step1: Rewrite inequalities as equations for boundary - lines

Rewrite $x - y=6$ and $x + y = 2$. For $x - y=6$, we can express $y=x - 6$. For $x + y=2$, we can express $y=-x + 2$.

Step2: Find the x - and y - intercepts of the boundary - lines

For $y=x - 6$: When $x = 0$, $y=-6$; when $y = 0$, $x=6$. For $y=-x + 2$: When $x = 0$, $y = 2$; when $y = 0$, $x=2$.

Step3: Determine which side of the boundary - lines to shade

For $x - y\geq6$, test a point not on the line, say $(0,0)$. Substitute into the inequality: $0-0=0
ot\geq6$, so we shade the side of the line $y=x - 6$ that does not contain the origin. For $x + y\leq2$, test the point $(0,0)$. Substitute: $0 + 0=0\leq2$, so we shade the side of the line $y=-x + 2$ that contains the origin.

Answer:

Graph the line $y=x - 6$ as a solid line (because the inequality is $\geq$) and shade the region below it that does not contain the origin. Graph the line $y=-x + 2$ as a solid line (because the inequality is $\leq$) and shade the region below it that contains the origin. The solution of the system of inequalities is the intersection of the two shaded regions.