linear equation in two variable

Question

√x + y = 3

x + √y =6

Answer 1

But these are not linear.....

second equation says: sqrt(y) = 6-x

y = (6-x)^2

substitutes into first equation:

sqrt(x) + (6-x)^2 = 3

sqrt(X) + 36 - 12x + x^2 = 3

x^2 - 12x + 33 = -sqrt(x)

(x^2 - 12x + 33)^2 = x

There are no rational solutions to this equation.

The irrational solutions are:

x = 3.777, 5.234, 6.649, 8.43

The only one that works is x=5.234

The intersection point is (5.234, 0.708)