SOLUTION: i need to solve this systems of equations using substitution X^2+Y^2=25 3X-4X=0

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Question 744166: i need to solve this systems of equations using substitution
X^2+Y^2=25
3X-4X=0

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The problem system%28X%5E2%2BY%5E2=25%2C3X-4X=0%29 is easy.
The only solution to 3X-4X=0 is X=0
3X-4X=0 --> -X=0 --> highlight%28X=0%29
Substituting X=0 into X%5E2%2BY%5E2=25 you get Y%5E2=25,
which has two solutions: highlight%28Y=5%29 and highlight%28Y=-5%29
The solutions to the system are the two pairs (0,5) and (0,-5), or
highlight%28system%28X=0%2CY=5%29%29 and highlight%28system%28X=0%2CY=-5%29%29

NOTE:
If the problem had been system%283X-4Y=0%2CX%5E2%2BY%5E2=25%29, the system could be solved similarly, with a little more work.
The answer is not pretty, so that was not the intended problem.
(Classroom problems are supposed to have pretty answers).
In that case, solving for X to substitute in the other equation we get
3X-4Y=0 --> 3X=4Y --> X=4Y%2F3 to substitute.
So you have
system%28X=4Y%2F3%2CX%5E2%2BY%5E2=25%29 --> %284Y%2F3%29%5E2%2BY%5E2=25 --> 16Y%5E2%2F9%2BY%5E2=25
At this point, I would multiply both sides to the equal sign times 9 to get rid of fractions. I would get
16Y%5E2%2B9Y%5E2=225 --> 16Y%5E2%2B9Y%5E2-225=0
That equation yields two ugly solutions for Y:

Each ugly Y can be substituted into X=4Y%2F3 to get the corresponding ugly X values X=%284%2F3%29%28%28-9+%2B-+3sqrt%281609%29%29%2F32%29=%28-3+%2B-+sqrt%281609%29%29%2F8
for a pair of ugly solutions.