SOLUTION: hi i was wondering how u do elimination using mulitplication, its in ch. 13 in the algebra 1 book on systems of equations and inequalities, please help thank you. question number o

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Question 31802: hi i was wondering how u do elimination using mulitplication, its in ch. 13 in the algebra 1 book on systems of equations and inequalities, please help thank you. question number one is shown below.
2x+6y=10
5x+3y=1
Answer by mbarugel(146) (Show Source):
You can put this solution on YOUR website!
Hello!
In order to do elimination using multiplication, the idea is to multiply one of the equations by a given number so that the coefficients of either x or y are the same in both equations. Let me illustrate:
You have:

Look at the coefficients of x. In the 1st equation it's 2; in the second one it's 5. You could multiply the first equation by 2.5 and you would get another 5 as the x coefficient in it. The first equation would become:

And the nyou would be ready to eliminate. Just subtract the 2nd equation from the 1st one, getting:

And now it's easy to find the value of y; and afterwards, of x.

In the example I showed you, I did a multiplication such that the x would 'disappear' after the subtraction. Of course, you could have done the same with y instead of x. The original system was:

Look at the coefficients of y: 6 in the 1st equation and 3 in the 2nd one. If you multiplied the 2nd equation by 2, you would get a '6y' in it. Let's do it:

And then you could subtract the 1st equation from this one, getting:

So now we can easily find x, and then y by simple subtitution.

I hope this helps!
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