Question

Solve the given system, using the substitution method.

y = 3x – 7
6x – 2y = 12

A.
(14, 12)

B.
(12, 14)

C.
There is no solution.

D.
There are an infinite number of solutions.

Answer 1

The general equation of a line is expressed as:

y = mx + b

We have to write the equations to this form to see whether from there we can conclude something.

y = 3x – 7 (1)
6x – 2y = 12 (2)
-2y = 12 - 6x
y = 3x -6

We can see that both equations have the same slope and different values of y-intercept. Therefore, they are parallel and would never meet.

The correct answer is option C, there is no solution.

Answer 2

y = 3x - 7 . . . . . (1)
6x - 2y = 12 . . . (2)

Putting (1) into (2) gives
6x - 2(3x - 7) = 12
6x - 6x + 14 = 12
14 = 12

Therefore, there is no solution.