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

Question

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

anonymous · Answer

HI there.  Would you like to learn the method or just get the answer?

anonymous · Answer

That just discourage people from learning.

anonymous · Answer

what does?

anonymous · Answer

Yes it does.

anonymous · Answer

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.

anonymous · Answer

Well try to teach me the method because I don't even know what the method is.

anonymous · Answer

The elimination method means we're trying to combine the equations in a way that makes one of the variables go away.

anonymous · Answer

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.

anonymous · Answer

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?

anonymous · Answer

Yes it does.

anonymous · Answer

Great.  so, first multiply the first equation through by -2; what do you get?

anonymous · Answer

-8x^2-6y^2=-24

anonymous · Answer

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.

anonymous · Answer

-3x^2=6

anonymous · Answer

Which would then be -3x^2/3=6/3 which is x^2=2, right?

anonymous · Answer

very close, I think you dropped a negative sign in that last step.

anonymous · Answer

(Make sure you copied the original problem correctly -- the problem you gave causes us to take the square root of a negative number)

anonymous · Answer

-3x^2=6 is correct though!