SOLUTION: Systems of Linear Equations: Solve Algebraically 2x+y=5 x^2+y^2=50

Question 433026: Systems of Linear Equations: Solve Algebraically
2x+y=5
x^2+y^2=50
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Systems of Linear Equations: Solve Algebraically
2x + y = 5
x^2 + y^2 = 50
:
Arrange the 1st equation for substitution
y = -2x+5
:
Replace y with (-2x+5) in the 2nd equation
x^2 + (-2x+5)^2 = 50
FOIL
x^2 + 4x^2 - 20x + 25 = 50
:
5x^2 - 20x + 25 - 50 = 0
:
5x^2 - 20x - 25 = 0
Simplify, divide by 5
x^2 - 4x - 5 = 0
Factor
(x-5)(x+1) = 0
Two solutions
x = 5
x = -1
:
When x=5; y = -2(5) + 5 = -5
When x=-1; y = -2(-1) + 5 = 7
:
:
Check both those solution sets in the 2nd equation
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