SOLUTION: Hi I have two systems of Equations that I can't seem to solve properly. Can someone provide complete solutions? A)x+y=5 X^2+Y^2=25 Right Answer is (0,5) (5,0) B)3X-4Y=

Algebra ->  College  -> Linear Algebra -> SOLUTION: Hi I have two systems of Equations that I can't seem to solve properly. Can someone provide complete solutions? A)x+y=5 X^2+Y^2=25 Right Answer is (0,5) (5,0) B)3X-4Y=      Log On


   

Question 937348: Hi I have two systems of Equations that I can't seem to solve properly.
Can someone provide complete solutions?
A)x+y=5
X^2+Y^2=25
Right Answer is (0,5) (5,0)
B)3X-4Y=25

X^2+Y^2=25
Right Answer is (3,-4)
I'm know I'm making some kind of stupid small error in my calculations.
Thanks in advance for your help
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

A)
you have here a system of two equations and you need to find x and y that satisfy each equation
x%2By=5........eq.1
x%5E2%2By%5E2=25........eq.2
-------------------------
start with
x%2By=5........eq.1...solve for x
x=5-y........eq.1a....substitute this in eq.2
%285-y%29%5E2%2By%5E2=25........eq.2
25-10y%2By%5E2%2By%5E2=25
2y%5E2-10y%2B25=25
2y%5E2-10y=25-25
2y%28y-5%29=0
solutions:
if 2y=0 => y=0
if %28y-5%29=0 => y=5
now find x
x=5-y........eq.1a if highlight%28y=0%29
x=5-0
highlight%28x=5%29

x=5-y........eq.1a if highlight%28y=5%29
x=5-5
highlight%28x=0%29
Answer is: (0,5) (5,0)

B)
3x-4y=25+
x%5E2%2By%5E2=25
_________________
3x=4y%2B25+
x=%284%2F3%29y%2B25%2F3+

x%5E2%2By%5E2=25
%28%284%2F3%29y%2B25%2F3%29%5E2+%2By%5E2=25
%2816%2F9%29y%5E2%2B2%284%2F3%29%2825%2F3%29y%2B9y%5E2%2F9=25
%2825%2F9%29y%5E2%2B%288%2F3%29%288%2A25%2F9%29y=25
25%2F9%28y%5E2%2B8y%2B25%29=25
cross%2825%29%28y%5E2%2B8y%2B25%29=cross%2825%29%2A9
y%5E2%2B8y%2B25=9
y%5E2%2B8y%2B25-9=0
y%5E2%2B8y%2B16=0
%28y%2B4%29%5E2=0%0D%0A%0D%0A%7B%7B%7Bhighlight%28y+=+-4%29

now find x:
x=%284%2F3%29y%2B25%2F3+
x=%284%2F3%29%28-4%29%2B25%2F3+
x=-16%2F3%2B25%2F3+
x=%2825-16%29%2F3+
x=9%2F3+
highlight%28x=3%29+

Answer is: (3,-4)