Ess, this took me a while to understand when I was first learning it. What we need is to make either the x's or y's to be opposites in order to add and cancel out.
3x - y = 5
6x - 2y = 10
How can we make the x's opposites? Multiplying the first equation by -2 would give us -6x, and -6x + 6x = 0. Bam.
The other thing we could do is multiply the first equation by -2 to get 2y, and 2y + (-2y) = 0.
Hold on, did I just repeat something. Multiplying the first equation by -2 cancels out both. In fact, it cancels out the constant, too!
-6x + 2y = -10
6x + 2y = 10
0 + 0 = 0
Since this is the case, these are both the same line and have an infinite number of answers.
