# Thread: Nonlinear Systems of Equations

1. ## Nonlinear Systems of Equations

Test Tommorow - Just can't seem to get the hang of it...

1) $\displaystyle y+x^2=4x$
$\displaystyle y+4x=16$

2) $\displaystyle x^2y=16$
$\displaystyle y^2-x^2+16=0$

3) $\displaystyle x-2y=2$
$\displaystyle y^2-x^2=2x+4$

Any help is greatly appreciated..thanks

2. Hello,

For 1), isolate y in the second equation and plug it in the first equation.

For 2), isolate y in the first equation, then plug it in the second and solve for X=x² like any quadratic equation

For 3), isolate x in the first and plug in the second.

3. Originally Posted by Ballplaya4237
Test Tommorow - Just can't seem to get the hang of it...

1) $\displaystyle y+x^2=4x$
$\displaystyle y+4x=16$

2) $\displaystyle x^2y=16$
$\displaystyle y^2-x^2+16=0$

3) $\displaystyle x-2y=2$
$\displaystyle y^2-x^2=2x+4$

Any help is greatly appreciated..thanks
For each of these, pick one of the equations and solve for one unknown. Then plug that into the other equation.

For example, the first one I would solve the bottom equation for y:
$\displaystyle y = -4x + 16$
and put that into the top equation:
$\displaystyle (-4x + 16) + x^2 = 4x$

Solve this for x and use that to solve for y.

-Dan

4. Okay, I managed to solve both numbers 1 and 3...

But, 2 still eludes me...

I messed up copying the first time - Here's the correct number 2 equation

2) $\displaystyle x^2y=16$
$\displaystyle x^2+4y+16=0$

5. This is the same princip : isolate y in the first equation and plug it in the second

Multiply the final equation by x², then substitute u=t² and solve it as a quadratic equation