x^2+y^2=25
y-x=1
and
x^2+y^2=5
xy=2
please help
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.