Question

Which statement about the solution to the following system of equations is true?

3x - 2y = 4
-6x + 4y = -8

A) There is no solution because the equation represents the same line
B) There is no solution because the equations have the same slope
C) There are infinitely many solutions because the lines have the same slope and different y-intercepts.
D) There are infinitely many solutions because the equations represent the same line

Answer 1

Let's solve and find out.

3x - 2y = 4
-6x + 4y = -8

To solve by elimination, multiply the top equation by 2 to cancel out y-terms.

2(3x - 2y = 4)
6x - 4y = 8

Now, add the equations together.

6x - 4y = 8
-6x + 4y = -8
+___________
0 - 0 = 0

Since we get that 0 = 0, this system has infinitely many solutions. Only graphs that represent the same line have infinitely many solutions, so...

Answer:
D) There are infinitely many solutions because the equations represent the same line