Question

identifying the solution
which point is a solution to the system?
(-4, -2)
(-1, -2)
(1, 4)
(2, 2)

Explanation:

Step1: Find equations of lines

First, for the dashed line: it has y-intercept $b=2$, slope $m=\frac{4-2}{1-0}=2$, so equation is $y=2x+2$.
For the solid line: it has y-intercept $b=-2$, slope $m=\frac{4-(-2)}{3-0}=2$, so equation is $y=2x-2$.
Wait, correction: the solution to a system is the intersection point, but these are parallel? No, check the options by substituting each point into both lines.

Step2: Test (-4,-2)

Substitute into $y=2x+2$: $-2=2(-4)+2=-8+2=-6$ → False.

Step3: Test (-1,-2)

Substitute into $y=2x+2$: $-2=2(-1)+2=0$ → False.

Step4: Test (1,4)

Substitute into $y=2x+2$: $4=2(1)+2=4$ → True.
Substitute into $y=2x-2$: $4=2(1)-2=0$ → False.

Step5: Test (2,2)

Substitute into $y=2x+2$: $2=2(2)+2=6$ → False.
Wait, correction: the shaded region is the solution set (system of inequalities). The dashed line is $y\leq2x+2$, solid line is $y\geq2x-2$. Test (1,4):
For $y\leq2x+2$: $4\leq4$ → True.
For $y\geq2x-2$: $4\geq0$ → True.

Answer:

(1, 4)