Question

homework: 7.4 hw - linear inequalities in two variables question list question 7 graph the solution of the s x - y ≥ 6 x + y ≤ 2 question 8 question 9 question 10 use the graphing tool to gr click to enlarge graph help me solve this view an example get more he

Explanation:

Step1: Rewrite inequalities as equations

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 - intercepts

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

Step3: Find the y - intercepts

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

Step4: Determine the shading

For $x - y\geq6$ (or $y\leq x - 6$), we test a point not on the line, say $(0,0)$. Since $0-0=0
geq6$, we shade the region below the line $y=x - 6$. For $x + y\leq2$ (or $y\leq -x + 2$), testing the point $(0,0)$ gives $0 + 0=0\leq2$, so we shade the region below the line $y=-x + 2$. The solution of the system is the intersection of the two shaded regions.

The graph would have a solid line for $y=x - 6$ (because of $\geq$) and a solid line for $y=-x + 2$ (because of $\leq$), with the appropriate shading as described above.

Answer:

Graph the solid line $y=x - 6$ and shade below it, graph the solid line $y=-x + 2$ and shade below it. The solution region is the intersection of the two shaded regions.