SOLUTION: Hi, I am completely confused on how to do this equation. Here's the equation: 3x+2y=A 5x+y=B I have tried to work the problem out and I don't even know how to start.I have

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Hi, I am completely confused on how to do this equation. Here's the equation: 3x+2y=A 5x+y=B I have tried to work the problem out and I don't even know how to start.I have      Log On


   

Question 549767: Hi, I am completely confused on how to do this equation. Here's the equation:
3x+2y=A
5x+y=B

I have tried to work the problem out and I don't even know how to start.I have to solve this by the multiplication method to find x and y. Is there anyway you could help me please? Thanks!
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
3x%2B2y=A (1)
5x%2By=B (2)

There are many ways to do this, elimination, substitution, matrix..... I will use the elimination method (multiplication method).
I will eliminate the y variable (although it doesn't matter which one you choose).
I will multiply Equation (1) by the constant in front of y in Equation (2) (which is 1). this does not change the equation.
I will then multiply the equation (2) by the constant in front of the y in equation (2) (which is 2). This leaves:
10x%2B2y=2B (3)

Now subtracting Equation (3) from Equatin (1) we are left with:
%283x%2B2y%29-%2810x%2B2y%29=A-2B
-7x=A-2B
And solving for x we get:
x=%28A-2B%29%2F-7

Now substituting this value for x into Equation (2) (Note: it doesn't matter where you sub this in, I choose equation (2) as y is already without a constant)
5%2A%28%28A-2B%29%2F-7%29%2By=B
y=B-5%2A%28%28A-2B%29%2F-7%29
y=B-5%2A%28%28A%2F-7%29-%282B%29%2F-7%29%29
y=B%2B%285%2F7%29%2AA%2B%282%2F7%29%2AB
y=%287%2F7%29%2AB%2B%285%2F7%29%2AA%2B%282%2F7%29%2AB
y=%289%2F7%29%2AB%2B%285%2F7%29%2AA

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Hopefully this helps a bit -- let me know if you are still unsure about anything
Romans 5:8