# Solution to 3 simultaneous equations

• Jan 9th 2011, 04:44 AM
bugatti79
Solution to 3 simultaneous equations
Folks,

I am struggling with this seemingly simple task of solving for s and t in terms of x and y to ultimately get u in terms of x and y.

$x=s+st/4+t^2/4$ (1)
$y=s+t$ (2)
$u=s/4+t/2$ (3)

My attempt is as follows: From eqn 1 find t, its a quadratic in t
$t=\frac{-s+- \sqrt {s^2+4(4x-4s)}}{2}$ (4)

From (2) find t $t=y-s$ (5)

Then equate 4 and 5???.... Im actually lost....

$s=\frac{4x-y^2}{4-y}$
$t=\frac{4(y-x)}{4-y}$
$u=\frac{8y-4x-y^2}{4(4-y)}$
• Jan 9th 2011, 05:12 AM
Quote:

Originally Posted by bugatti79
Folks,

I am struggling with this seemingly simple task of solving for s and t in terms of x and y to ultimately get u in terms of x and y.

$x=s+st/4+t^2/4$ (1)
$y=s+t$ (2)
$u=s/4+t/2$ (3)

My attempt is as follows: From eqn 1 find t, its a quadratic in t
$t=\frac{-s+- \sqrt {s^2+4(4x-4s)}}{2}$ (4)

From (2) find t $t=y-s$ (5)

Then equate 4 and 5???.... Im actually lost....

$s=\frac{4x-y^2}{4-y}$
$t=\frac{4(y-x)}{4-y}$
$u=\frac{8y-4x-y^2}{4(4-y)}$

From (2)

$t=y-s$

Substitute into (1)

$\displaystyle\ x=s+\frac{s(y-s)+(y-s)^2}{4}\Rightarrow\ 4x=4s+sy-s^2+y^2-2sy+s^2$

$\Rightarrow\ 4x=y^2+s(4-y)$

from which "s" can be isolated.