# Help with nonlinear systems!

• April 15th 2008, 09:11 PM
LVCam
Help with nonlinear systems!
x^2+y^2=25
y-x=1

and

x^2+y^2=5
xy=2

• April 15th 2008, 10:14 PM
TwistedOne151
In both cases, solve the second equation for one variable in terms of the other, and then substitute into the first. For example, with:
$x^2+y^2=25$
$y-x=1$
we can solve the second for y:
$y=1+x$
and substituting into the first equation:
$x^2+(1+x)^2=25$
$2x^2+2x+1=25$
$2x^2+2x-24=0$
$x^2+x-12=0$
$(x-3)(x+4)=0$
so x=3 or x=-4, and substituting into the second equation, we get y=4 or y=-3 respectively, so we have (3,4) and (-4,-3) as solutions.

The second can be solved similarly.

--Kevin C.
• April 16th 2008, 07:05 AM
LVCam
thanks twisted