Example 05 - Simultaneous Non-Linear Equations of Two Unknowns

From Equation (1)
$x = 6 - 2y$   ←   Equation (3)
 

Substitute x = 6 - 2y to Equation (2)
$\sqrt{6 - 2y} + \sqrt{y} = 3$

$\sqrt{6 - 2y} = 3 - \sqrt{y}$
 

Square both sides
$6 - 2y = 9 - 6\sqrt{y} + y$

$6\sqrt{y} = 3 + 3y$

$2\sqrt{y} = 1 + y$
 

Square again both sides
$4y = 1 + 2y + y^2$

$y^2 - 2y + 1 = 0$

$(y - 1)^2 = 0$

$y = 1 ~ \text{ twice}$
 

From Equation (3)
$x = 6 - 2(1) = 4$
 

Hence, x = 4 and y = 1           answer