Question

how do i solve the nonlinear system of equation
2xsquared+y squared=6
xsquared-4ysquared= -15

Answer 1

Suppose we have two equations, without too much imagination (I) and (II) which are, respectively\[2x ^{2}+y ^{2}=6\]\[x ^{2}-4y ^{2}=-15\]Multiply (II) by -2 to give us (II)*\[-2x ^{2}+8y ^{2}=30\]Now combine by addition (I) + (II)*
\[9y ^{2}=36\]So\[y=\pm2\]Substitute to get \[x=\pm1\]Our solutions are\[(x,y)=(-1,-2),(-1,2),(1,-2),or(1,2)\]