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solve the system of equations by using the elimination method. {4x^2+3y^2=12 {5x^2+6y^2=30

Mathematics
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HI there. Would you like to learn the method or just get the answer?
That just discourage people from learning.
what does?

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Yes it does.
I only teach methods, I don't give out answers. But some people get mad when I try to teach. That's why I ask first.
Well try to teach me the method because I don't even know what the method is.
The elimination method means we're trying to combine the equations in a way that makes one of the variables go away.
If you add the two equations together (e.g. add the left sides together, and add the right sides together), then you'll get a different equation as a result, which is still true. So the idea is to find a way to eliminate one of the variables by hoping that when we add the two equations together, one of the variables will cancel.
In this case, the easiest strategy is to multiply the first equation by -2. That way, the 3y^2 will turn into -6y^2, which will then cancel with the +6y^2 in the second equation when we add the two together. Does that make sense?
Yes it does.
Great. so, first multiply the first equation through by -2; what do you get?
-8x^2-6y^2=-24
exactly right!! Now add that equation to the second equation (5x^2+6y^2=30). Remember, "adding" means, all the left-hand side terms get added to form the final left-hand-side term, and all the right-hand-side terms form a single right-hand side term. In other words, a + b = c added to d + e = f gives you a + b + d + e = c + f When you add the two equations in your problem together, you should find the Y terms cancel out.
-3x^2=6
Which would then be -3x^2/3=6/3 which is x^2=2, right?
very close, I think you dropped a negative sign in that last step.
(Make sure you copied the original problem correctly -- the problem you gave causes us to take the square root of a negative number)
-3x^2=6 is correct though!

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