Originally Posted by

**mathgeek777** I have this system:

$\displaystyle x^2+2y^2-4x+6y-5=0$

$\displaystyle -x+y-4=0$

And I have to find the intersecting points of the two equations by using substitution and only substitution.

I solved the bottom equation for y getting $\displaystyle y=x-4$. From there, this is how I progressed:

$\displaystyle x^2+2(x+4)^2-4x+6(x{\color{red}+}4)-5=-$

$\displaystyle x^2+2(x^2+8x+16)-4x+6x+24-5=0$

$\displaystyle x^2+2x^2+16x+32-4x+6x+24-5=0$

Combining like terms:

$\displaystyle 3x^2+18x+51=0$

Pulling out a 3 gives me:

$\displaystyle 3(x^2+6x+17)=0$

From here, I'm not sure what to do. Am I on the right track or am I doing this completely wrong? If the latter, please explain to me where I made an error so it doesn't happen again.

Thank you.