SOLUTION: solve the system x^2+y^2=37, 3x-9=y there are two solutions: (x1,y1) and (x2,y2) Evaluate x1+y1+x2+y2=

Question 1117128: solve the system x^2+y^2=37, 3x-9=y there are two solutions: (x1,y1) and (x2,y2)
Evaluate x1+y1+x2+y2=
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
solve the system x^2+y^2=37, 3x-9=y
replace (3x-9) for y in the first equation
x^2 + (3x-9)^2 = 37
FOIL (3x-9)(3x-9)
x^2 + 9x^2 -27x - 27x + 81 = 37
10x^2 - 54x + 81 - 37 = 0
10x^2 - 54x + 44 = 0
simplify, divide by 2
5x^2 - 27x + 22 = 0
Factors to
(5x-22)(x-1) = 0
two solutions
5x = 22
x = 22/5
x = 4.4
and
x = 1
:
there are two solutions:
y = 3(4.4)-9
y = 4.2
and
y = 3(1) - 9
y = -6
:
(x1,y1) and (x2,y2)
4.4, 4.2 and 1,-6
:
:
Check
4.4^2 + .2^2 = 37
and
1^2 + -6^2 = 37
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