Question

Two lines, C and D, are represented by the equations given below:

Line C: y = x + 12
Line D: y = 3x + 2

Which of the following shows the solution to the system of equations and explains why?

(4, 14), because one of the lines passes through this point
(4, 14), because the point lies between the two axes
(5, 17), because both lines pass through this point
(5, 17), because the point does not lie on any axis

Answer 1

Set the equations equal to each other to find the value of x. 

x + 12 = 3x + 2

Subtract x from both sides.

12 = 2x + 2

Subtract 2 from both sides.

10 = 2x

Divide by 2 on both sides to find x.

x = 5

Now you know your answer is either the third option or fourth option. 

Plug 5 in for x in one of the equations given to find y. 

y = 5 + 12
y = 17

If you plug in both x and y to the second equation, they come out equal to each other, your answer is (5, 17), because both lines pass through this point.

Answer 2

Answer:

The Answer is C.  (5, 17), because both lines pass through this point

Hope This Helps!