# Thread: Simultaenous Eq. with two unknowns

1. ## Simultaenous Eq. with two unknowns

(root)x+y=11, x+(root)y=7

Can anyone help me to find the values of X and Y? Thanks.

2. ## Possible Solution

Originally Posted by cheque
(root)x+y=11, x+(root)y=7

Can anyone help me to find the values of X and Y? Thanks.
Well, I just guessed and checked and found that x = 4 and y = 9.

Equation 1: root(4) + 9 = 2 + 9 = 11 This checks out
Equation 2: 4 + root(9) = 4 + 3 = 7 This also checks out

I'll try to find the actual method for arriving at this conclusion.

3. Originally Posted by ajj86
Well, I just guessed and checked and found that x = 4 and y = 9.

Equation 1: root(4) + 9 = 2 + 9 = 11 This checks out
Equation 2: 4 + root(9) = 4 + 3 = 7 This also checks out

I'll try to find the actual method for arriving at this conclusion.
Yeah, I got the answer through brute-forcing too. . Take your time and please update on your progress.

4. $\sqrt(x) = 11-y$*
$x = 121 - 22y +y^2$
$\sqrt(y) = 7-x$
$y = 49 - 14x +x^2$
$1444 - 1065 x + 272 x^2 - 28 x^3 + x^4 =0$*
Try the factor of 1444 as roots. You should not search for a long time.
I keep thinking there must be a more elegant solution but this is one.