x^2+y^2=25

y-x=1

and

x^2+y^2=5

xy=2

please help (Thinking)

Printable View

- Apr 15th 2008, 08:11 PMLVCamHelp with nonlinear systems!
x^2+y^2=25

y-x=1

and

x^2+y^2=5

xy=2

please help (Thinking) - Apr 15th 2008, 09:14 PMTwistedOne151
In both cases, solve the second equation for one variable in terms of the other, and then substitute into the first. For example, with:

$\displaystyle x^2+y^2=25$

$\displaystyle y-x=1$

we can solve the second for y:

$\displaystyle y=1+x$

and substituting into the first equation:

$\displaystyle x^2+(1+x)^2=25$

$\displaystyle 2x^2+2x+1=25$

$\displaystyle 2x^2+2x-24=0$

$\displaystyle x^2+x-12=0$

$\displaystyle (x-3)(x+4)=0$

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. - Apr 16th 2008, 06:05 AMLVCam
thanks twisted