Solve the system of equations by using graphical methods.
A) (-5,5)
B) (-5,-3)
C) (-2,5)
D) (-2,-5)
E) There is no solution to the equations.

Question

Solve the system of equations by using graphical methods. ​  ​
A) (-5,5) 
B) (-5,-3) 
C) (-2,5) 
D) (-2,-5) 
E) There is no solution to the equations.

Quizplus · Accepted Answer

To solve this system of equations graphically, we will plot the two equations on the same coordinate system and look for the point of intersection.

y = x + 7

can be graphed by plotting the point (0,7) and then using the slope of 1 (rise 1, run 1) to find additional points.

y = -\frac{1}{2}x + 6

can be graphed by plotting the point (0,6) and then using the slope of -\frac{1}{2} (rise -1, run 2) to find additional points.

When we graph these two lines on the same coordinate system, we get the following:

graph{y=x+7 [-10, 10, -5, 10, green]}graph{y=-x/2+6 [-10, 10, -5, 10, blue]}

We can see that the lines intersect at the point (-2,5). Therefore, the solution to the system of equations is:

x = -2
y = 5

and the correct choice is C) (-2,5).

Solve the System of Equations by Using Graphical Methods