SOLUTION: please help me solve this equation x^2+2xy−y^2=−17 x^2−y^2=−45

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Question 926377: please help me solve this equation
x^2+2xy−y^2=−17
x^2−y^2=−45
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B2xy-y%5E2=-17..........eq.1
+x%5E2-y%5E2=-45..........eq.2
_____________________________________subtract eq.2 from eq.1
x%5E2%2B2xy-y%5E2-%28x%5E2-y%5E2%29=-17-%28-45%29
cross%28x%5E2%29%2B2xy-cross%28y%5E2%29-cross%28x%5E2%29%2Bcross%28y%5E2%29=-17%2B45
2xy+=28
xy+=14.....solve for x
x+=14%2Fy.....eq.1a
go to +x%5E2-y%5E2=-45..........eq.2, substitute x+=14%2Fy

+%2814%2Fy%29%5E2-y%5E2=-45....solve for y

+14%5E2%2Fy%5E2-y%5E2=-45
+196%2Fy%5E2=y%5E2-45
196=y%5E2%28y%5E2-45%29
196=y%5E4-45y%5E2
0=y%5E4-45y%5E2-196
y%5E4%2B2y%5E2-49y%5E2-196=0
%28y%5E4%2B2y%5E2%29-%2849y%5E2%2B196%29=0
y%5E2%28y%5E4%2B2%29-49%28y%5E2%2B4%29=0
%28y%5E2-49%29%28y%5E2%2B4%29=0
%28y%5E2-7%5E2%29%28y%5E2%2B4%29=0
%28y-7%29%28y%2B7%29%28y%5E2%2B4%29=0
solutions:
if y-7=0 =>y=7
if y%2B7=0=>y=-7
if y%5E2%2B4=0=>y%5E2=-4=>y=sqrt%28-4%29=>y=2i or y=-2i; complex solutions

so, x+=14%2Fy will be
real solutions:
x+=14%2F7=> x+=2 if y=7
and
x+=14%2F-7=> x+=-2 if y=-7
complex solutions:
x+=14%2F2i=> x+=7i if y=2i
and
x+=14%2F-2i=> x+=-7i if y=-2i