Solve for x and y. sqrt{x} + y = 7 x + sqrt{y} = 11
sqrt(x)+ y = 7..............1) x + sqrt(y) = 11...........2) -------------------------------------isolate sqrt sqrt(x) = 7-y..............1) sqrt(y) = 11-x...........2) --------------------------------square both sides x = (7-y)^2..............1) y = (11-x)^2...........2) ---------------------------------------- x = y^2 - 14 y + 49..............1) y = x^2 - 22 x + 121...........2) ------------------------------------- substitute x from eq. 1) y = (y^2 - 14 y + 49)^2 - 22 (y^2 - 14 y + 49) + 121...........2), solve for y 0= y^4 - 28 y^3 + 272 y^2 - 1064 y + 1444 -y y^4 - 28 y^3 + 272 y^2 - 1065 y + 1444=0....factor (y - 4) (y^3 - 24 y^2 + 176 y - 361) = 0 one solution: y=4 y^3 - 24 y^2 + 176 y - 361= 0 roots are y≈3.4156 y≈9.8051 y≈10.779 we dont use approximate values so, solution is x=9, y=4 intersection point: (9,4)