# Thread: Systems of nonlinear equations in two variables- Need help with 2 problems

1. ## Systems of nonlinear equations in two variables- Need help with 2 problems

Can you please me with the following problems:

Solve by the method of your choice.

x^2+y^2=50
(x-7)^2+y^2=1

I tried to find a variable that I could isolate and I wasnt sure what to mulitply by in order to get a variable to isolate.

x^2+y^2=29
-8x+y^2=41

this is as far as I got:

8(x^2+y^2=29)

now I got:

8x^2+y^2=232
-8x+y^2=41

but I still cant isolate anything.

2. Originally Posted by soly_sol
Can you please me with the following problems:

Solve by the method of your choice.

x^2+y^2=50
(x-7)^2+y^2=1
Typically in Physics we tend to use the "substitution method." But in this particular case the substitution method is going to rather messy. What I would do is subtract the second equation from the first:
$\displaystyle (x^2+y^2) - (x-7)^2+y^2) = 50 - 1$

$\displaystyle x^2 - (x - 7)^2 = 49$
and go from there.

-Dan

3. Originally Posted by soly_sol
x^2+y^2=29
-8x+y^2=41
Watch your multiplication: You have to multiply everything on both sides of the equation by 8, not just one term.

Here you could use substitution. Solve the second equation for x:
$\displaystyle x = \frac{1}{8}(y^2 - 41)$

Then insert this value of x into the first equation:
$\displaystyle \left ( \frac{1}{8}(y^2 - 41) \right ) ^2+y^2=29$

It'll take a while, but its doable.

The other way is faster: just subtract both equations again:
$\displaystyle (x^2+y^2) - ( -8x+y^2) = 29 - 41$

$\displaystyle x^2 + 8x = -12$
etc.

-Dan