Solve the system: 9x^2 + 4(y-2)^2 = 36 x^2 = 2y

1 Answer | Add Yours

lfryerda's profile pic

Posted on

To solve the system



we need to substitute the second equation into the first, then solve the subsequent quadratic equation.

Upon substitution, we see that

`9(2y)+4(y-2)^2=36`   now expand

`18y+4(y^2-4y+4)=36`  expand again

`18y+4y^2-16y+16=36`  collect like terms

`4y^2+2y-20=0`   divide by 2

`2y^2+y-10=0`   factor left side

`(2y+5)(y-2)=0`   now solve to get:

`y=2` or `y=-5/2` .

Now we need to substitute the y-values into the original equations, but since `x^2=2y` , this means that `y>0` , so the only possible solution is `y=2` .

Now solving for x, we get 




This means there are two solutions `x=2` , `y=2` and `x=-2` , `y=2` . As a check, note that `9(+-2)+4(2-2)^2=36` .

We’ve answered 331,126 questions. We can answer yours, too.

Ask a question