SOLUTION: Solve the system of equations: the 2 given non linear equations are below and I'm not sure where to begin? {{{ (2/x^2)+(3/y^2)=(5/6)) }}} and {{{ (4/x^2)-(9/y^2)=0) }}}

Algebra ->  Systems-of-equations -> SOLUTION: Solve the system of equations: the 2 given non linear equations are below and I'm not sure where to begin? {{{ (2/x^2)+(3/y^2)=(5/6)) }}} and {{{ (4/x^2)-(9/y^2)=0) }}}       Log On


   

Question 1079336: Solve the system of equations:
the 2 given non linear equations are below and I'm not sure where to begin?
+%282%2Fx%5E2%29%2B%283%2Fy%5E2%29=%285%2F6%29%29+ and +%284%2Fx%5E2%29-%289%2Fy%5E2%29=0%29+
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +%282%2Fx%5E2%29%2B%283%2Fy%5E2%29=%285%2F6%29%29+
(2) +%284%2Fx%5E2%29-%289%2Fy%5E2%29=0%29+
--------------------------------
Multiply both sides of (1) by +3+
and add the equations
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(1) +%286%2Fx%5E2%29%2B%289%2Fy%5E2%29=%285%2F2%29%29+
(2) +%284%2Fx%5E2%29-%289%2Fy%5E2%29=0%29+
--------------------------------
+10%2Fx%5E2+=+5%2F2+
+10%2Fx%5E2+=+10%2F4+
+x%5E2+=+4+
+x+=+2+
+x+=+-2+
--------------------------
Plug this result back into (1) or (2)
(2) +%284%2Fx%5E2%29-%289%2Fy%5E2%29=0%29+
(2) +%284%2F4%29-%289%2Fy%5E2%29=0%29+
(2) +1+-+9%2Fy%5E2+=+0+
(2) +9%2Fy%5E2+=+1+
(2) +9%2Fy%5E2+=+9%2F9+
(2) +y%5E2+=+9+
(2) +y+=+3+
(2) +y+=+-3+
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I believe the solutions are:
( 2,3 ), ( 2.-3 ) and
( -2,3 ), ( -2,-3 )