Questions: Graph the solution of the system of linear inequalities. y ≥ -x + 4 y ≤ 2x + 6

Solution Steps

For $y = -x + 4$, If $x=0$, then $y=4$. Thus, the point is $(0,4)$. If $y=0$, then $0 = -x+4$, or $x=4$. Thus, the point is $(4,0)$.

For $y = 2x + 6$, If $x=0$, then $y=6$. Thus, the point is $(0,6)$. If $y=0$, then $0 = 2x+6$, or $x=-3$. Thus, the point is $(-3,0)$.

Plot the points found in Steps 1 and 2 on the graph and draw a solid line for each since both are $\le$ or $\ge$. For the first inequality, shade the region above the line $y=-x+4$. For the second inequality, shade the region below the line $y=2x+6$.

Final Answer: