x^2 + y^2 = 25 and
x^2 + 7y = 37
multiply the second one with -1 you will have
$\displaystyle -x^2-7y=-37$
find the sum of that and this
$\displaystyle x^2+y^2=25$
$\displaystyle -x^2-7y+x^2+y^2=27-37$
$\displaystyle y^2-7y+10=0$
$\displaystyle (y-2)(y-5)=0$
$\displaystyle y-2=0...y=2 , y-5=0...y=5$
sub these values of y in one of the equation $\displaystyle x^2+7y=37$ or $\displaystyle x^2+y^2=25$ you will have the values of x this is elimination you eliminate x ...