# Thread: Elimination method in non-linear equation

1. ## Elimination method in non-linear equation

x^2 + y^2 = 25 and
x^2 + 7y = 37

2. Originally Posted by galanm
x^2 + y^2 = 25 and
x^2 + 7y = 37
multiply one of the equation with -1 and add it to the other one

3. Originally Posted by galanm
x^2 + y^2 = 25 and
x^2 + 7y = 37
Substitute x^2 = 37 - 7y from the second equation into the first equation and solve the quadratic equation for y.

4. The instructions state to use the elimintation method.

5. Originally Posted by galanm
The instructions state to use the elimintation method.
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 ...