SOLUTION: Solve the system of equations {{{ x^2 }}} + {{{ y^2 }}} = 169 {{{ x^2 }}} -8y = 104 Could you please prvide me with a detailed explanation of how you achieved the solution

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the system of equations {{{ x^2 }}} + {{{ y^2 }}} = 169 {{{ x^2 }}} -8y = 104 Could you please prvide me with a detailed explanation of how you achieved the solution      Log On


   

Question 188829: Solve the system of equations
+x%5E2+ + +y%5E2+ = 169
+x%5E2+ -8y = 104

Could you please prvide me with a detailed explanation of how you achieved the solution. Thanks!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + y^2 = 169
x^2 - 8y = 104
-------------------Subtraction eliminates x^2
y^2 + 8y = 65
A quadratic equation:
y^2 + 8y - 65 = 0
Factors to:
(y + 13)(y - 5) = 0
Two solutions
y = -13
y = +5
;
Find x when y = -13 using the 1st equation:
x^2 + (-13)^2 = 169
x^2 + 169 = 169
x^2 = 169 - 169
x^2 = 0
x = 0
when y = 5
x^2 + 5^2 = 169
x^2 = 169 - 25
x^2 = 144
x = sqrt%28144%29
x = +/-12
:
:
Check solutions x=0, y=-13, in 2nd equation
0 - 8(-13) = 104
0 + 104 = 104
:
Check solutions x=+/-12, y=5 in 2nd equation
12^2 - 8(5) = 104
144 - 40 = 104
:
Graphing it,we can see the actual solutions are; x=-12, y=5 and x=+12, y=5: