Solution:
Step 1: Find the equation of the line in the graph.
Two points the line pass through are (0, -4) and (2, -3)
Thus,
[tex]\begin{gathered} x_1=0,y_1=-4 \\ x_2=2,y_2=-3 \end{gathered}[/tex][tex]\begin{gathered} The\text{ equation of the line can be calculated with the formula} \\ \frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \\ \\ \frac{-3-(-4)}{2-0}=\frac{y-(-4)}{x-0} \\ \\ \frac{-3+4}{2}=\frac{y+4}{x} \\ \frac{1}{2}=\frac{y+4}{x} \end{gathered}[/tex][tex]\begin{gathered} 2(y+4)=x \\ 2y+8=x \\ 2y=x-8 \end{gathered}[/tex]
The equation of the graph is 2y = x - 8
Step 2:
Solve the two equations simultaneously to detemine the solution to the systems of equations
2y = x - 8 ------------------------equation (1)
y = -x + 2 ----------------------equation (2)
Add both equations to eliminate x
2y + y = x - 8 + (-x) + 2
3y = x -8-x+2
3y = -8 + 2
3y = -6
y = -6/3
y = -2
Substitute y = -2 into equation (2)
y = -x + 2
-2 = -x + 2
-2 -2 = -x
-4 = -x
-x = -4
Divide both sides by -1
x = 4
Hence, the solution to the system of equations is (4, -2)
The correct option is option D
