SOLUTION: What is the solution set of the system of equations x+y=5 and y=x^2-25

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Question 753944: What is the solution set of the system of equations x+y=5 and y=x^2-25
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
+x%2By=5.....eq.1
y=x%5E2-25......eq.2
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+x%2By=5.....eq.1...solve for y
+y=-x%2B5....eq.1a.......substitute in eq.2

y=x%5E2-25......eq.2
-x%2B5=x%5E2-25.....solve for x
0=x%5E2%2Bx-5-25
or x%5E2%2Bx-30=0.....write x as 6x-5x
x%5E2%2B6x-5x-30=0....group
%28x%5E2%2B6x%29-%285x%2B30%29=0
x%28x%2B6%29-5%28x%2B6%29=0
%28x-5%29%28x%2B6%29=0......use zero product rule to find solutions
if x-5=0 => x=5
if x%2B6=0 => x=-6
now find y
if highlight%28x=5%29 => +y=-5%2B5=> +highlight%28y=0%29
if highlight%28x=-6%29 => +y=-%28-6%29%2B5=> +y=6%2B5 => +highlight%28y=11%29