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