Could anybody Help me with this simultaneous equation please

Barry247

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Many thanks to those who helped me solve my last problem, I would appreciate any suggestions on this last question. I have listed the steps below that I have tried

Any help would be gratefully appreciated

Question from my A level maths text book

Solve this pair of simultaneous equation by eliminating either the terms in x^2 or the terms in Y^2?

X^2 +Y^2 -3X =9 (Eq 1)

X^2 - Y^2 +X + 4Y = 3 (Eq 2)

Adding both together

2X^2 -2X +4Y =12

Second attempts Now I get this

2x^ -2x -12 = -4y

2x^2 -2x -12 /-4 =y


-1/2x^2 - 1/2x -3 =y


Therefor

x^2 +(-1/2x^2 -1/2x -3)^2 -3x = 9

Is this correct so far?






Second attempt

Multiply equation 2 by 3

3X^2 - 3Y^2 +3X +12Y = 9

Eq 1 =Eq 2

3X^2 - 3Y^2 +3X + 12 Y = X^2 +Y^2 -3X


3X^2 - 3Y^2 + 3X +12 Y - X^2 -Y^2 +3X =0

3X^2 - X^2 +6X - 3Y^2 - Y^2 +12Y = 0

2X^2 +6X -4Y^2 +12Y = 0

X^2 + 3X -2Y^2 +6Y = 0

X^2 +3X = 2Y^2 - 6Y


Can not get x or y on its own

I can not get any further, I have tried for many hours, I have solved 17 equations on the page of my text book but I seem to be stuck on the last one


Would appreciate any suggestions

Many thanks in advance

Barry
 
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Solve this pair of simultaneous equation by eliminating either the terms in x^2 or the terms in Y^2?

X^2 +Y^2 -3X =9 (Eq 1)

X^2 - Y^2 +X + 4Y = 3 (Eq 2)

Adding both together

2X^2 -2X +4Y =12

Since they said to eliminate y^2, I would do that, which is just what you did. (Or you could subtract the equations to eliminate x^2.)

Now what?

Well, since there is no y^2, you can solve this for y and substitute in one of the equations. That will eliminate y entirely.

It will look pretty bad at first, but you'll find that it simplifies down nicely. If it doesn't, try a different substitution, or a different first step; in algebra, you don't always know ahead of time what will work best. But the strategy suggested here (get rid of the worst part of the equation and see if it helps) is often a good one.

By the way, you really shouldn't be mixing cases; I'd use x and y everywhere, not X and Y.
 
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X^2 +Y^2 -3X =9 (Eq 1)

X^2 - Y^2 +X + 4Y = 3 (Eq 2)

Adding both together

2X^2 -2X +4Y =12

No way of getting X Or Y on its own
...but there is :)

1st step, divide by 2:
x^2 - x + 2y = 6
2nd step, isolate y:
y = (6 + x - x^2) / 2

Substitute in (Eq 1)

You'll find that as DrP said, terms will cancel "kinda nicely"!

NOTE: use lowercase x and y...else we'll sue you:p
 
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