SOLUTION: Use any method to solve the nonlinear system. (If there is no solution, enter NO SOLUTION.) −x^2 + y = 8 8y= −x Could someone assist in explaining how to to cor

Algebra ->  College  -> Linear Algebra -> SOLUTION: Use any method to solve the nonlinear system. (If there is no solution, enter NO SOLUTION.) −x^2 + y = 8 8y= −x Could someone assist in explaining how to to cor      Log On


   

Question 1129923: Use any method to solve the nonlinear system. (If there is no solution, enter NO SOLUTION.)
−x^2 + y = 8
8y= −x
Could someone assist in explaining how to to correctly solve the equation as my previous answer was wrong. Previously I got: (x, y)= (-1/6 + i +sqrt%28+2047+%29+/ 16) , (1/ 128 -i+sqrt%28+2047+%29+/ 128).

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

-x%5E2+%2B+y=+8........eq.1
8y=+-x+........eq.2
--------------------------
8y=+-x+........eq.2=> -8y=+x+.......substitute in .eq.1
-%28-8y%29%5E2+%2B+y=+8........eq.1
-64y%5E2+%2B+y=+8
0=64y%5E2-y%2B+8

y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A64%2A8%29%29%2F%282%2A64%29+
y=+%281+%2B-+sqrt%28+1-2048%29%29%2F128+
y=+%281+%2B-+sqrt%28+-2047%29%29%2F128+
y=+%281+%2B-+sqrt%28+2047%29%2Ai%29%2F128+

y=+%281%2F128%29%281+%2B-+sqrt%28+2047%29%2Ai%29+

solutions:
highlight%28y=+%281%2F128%29%281+%2B+sqrt%28+2047%29%2Ai%29%29+
or
highlight%28y=+%281%2F128%29%281+-+sqrt%28+2047%29%2Ai%29%29+

and x will be
eq.2=> x=-8y+
x=-8%281%2F128%29%281+%2B+sqrt%28+2047%29%2Ai%29+
x=-cross%288%29%281%2Fcross%28128%2916%29%281+%2B+sqrt%28+2047%29%2Ai%29+
highlight%28x=-%281%2F16%29%281+%2B+sqrt%28+2047%29%2Ai%29%29+
or
highlight%28x=-%281%2F16%29%281+-+sqrt%28+2047%29%2Ai%29%29+