Solve the system by using elimination or elimination with multiplication.
3x - 2y = 9 and -3x + 2y = -9

Question

Solve the system by using elimination or elimination with multiplication.
3x - 2y = 9 and -3x + 2y = -9

whpalmer4 · Answer

What do you get if you add both equations together?

anonymous · Answer

I did the equation and I think the answer is (1,-3) or infinintly many solutions. :)

whpalmer4 · Answer

What do you get if you add those two equations together?

whpalmer4 · Answer

$$3x-2y=9$$$$-3x+2y=-9$$---------------3x-3x-2y+2y=9-9\]$$0=0$$
If you get a true statement like that, it means the lines are identical and there are infinitely many solutions, of which $(1,-3)$ is one.  

If you get a false statement, such as happens here:
$$3x-2y=9$$$$-3x+2y=-10$$-----------------$$3x-3x-2y+2y=9-10$$$$0=-1$$That means the lines are parallel, and there are no solutions.

anonymous · Answer

so the answer is no solution?

whpalmer4 · Answer

For your problem, we got 0=0 after adding the two equations, so the answer there is infinitely many solutions.   

I then gave a very similar example where we got 0 = -1, to illustrate a case where the correct answer would be "no solution".