Question

If you wanted to eliminate the y variable by adding the two equations in the following system, what could be your first step?

5x − 6y = 6
x − y = 12

Add the two equations together

Multiply the second equation by −6

Multiply the first equation by −6

Multiply the second equation by 6

Answer 1

You want the equations to line up nicely by getting one term to show up in both equations. Ideally you do not want fractions if you can avoid them.

So here's what you do to solve these equations:
5x − 6y = 6
x − y = 12

Multiply the second equation by 6:
5x - 6y = 6
6x - 6y = 72

Then you can put y on one side and x on the other:
-6y = 6 - 5x
-6y = 72 - 6x

Reverse the polarity:
6y = 5x - 6
6y = 6x - 72

Now remember y = y, and x = x, therefore:
5x - 6 = 6x - 72

Now put x on one side:
5x - 6x = -72 + 6
-x = -66
x = 66

Answer 2

And apparently I can't edit my answer, so remember x is not actually equal to 66, because 6y = 66 therefore x = 11, actually.

Answer 3

I really need sleep.

Answer 4

I'm still not sure what the answer is :'( @Rav

Answer 5

The answer is in my first post.

"Multiply the second equation by 6"

Answer 6

lol okay thanks(: