SOLUTION: using the elimination method how can i solve the system for x and y in the problem 6x+y=51 & x-2y=2 does the -2y "elimintate" with the positive y? I'm confused please help.

Click here to see ALL problems on Systems-of-equations

Question 613156: using the elimination method how can i solve the system for x and y in the problem 6x+y=51 & x-2y=2
does the -2y "elimintate" with the positive y? I'm confused please help.

Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website!
WORDY EXPLANATION:
Elimination refers to making a linear combination of the equations so as to eliminate one variable. By "making a linear combination" we mean multiplying each equation by a factor (a number) and then adding. The factors used for both equations are usually different, and one could be negative. If we are lucky, one or both factors would be 1, so we do not need to multiply. We choose those factors so that the terms for one of the variables end up being opposites in the multiplied equations. That "eliminates" the variable when we add.
In the system
I would multiply the first equation times 2, to get
(with a +2y term that is the opposite of the -2y term in the other equation).
Then I would add that to the second equation (multiplied by 1) to get
which simplifies into -->-->
That means that the original system is equivalent to a system made up of and one of the original equations. Of course, I would pick

and then I would continue working with the very easy system

WHAT YOU WOULD WRITE:
It depends on what format your teacher prefers, and how strict that preference is. You could write something like this:

first equation times 2

______
--> -->

AND FROM THERE ON:
At this point you could say that you substitute 8 for x in to get
and solve that.
Otherwise, you could say that you continue combining equations, multiplying times (-1) to get
and then adding (multiplied times 1) to get
-->-->-->