x^1/2+y=11,x+y^1/2=7

Hello student,
Please find the answer to your question below
From(1): x^(1/2) = 7 - y ,
Letx^(1/2)+y=11...........(1)
x+y^(1/2)=7..........(2)
Squaring both sides:
x = (7-y)^2 = y^2 - 14y + 49,
Goto (2): y^2 - 14y + 49 + y^(1/2) = 11,
Let w = y^1/2, so y = w^2,
so we have w^4 - 14 w^2 + w + 38 = 0,
Use syntheic division,we have
w=2 as a factor
Hence,(w-2)(w^3 + 2w^2-10w -19) = 0.
Unfortunately, we cannot factor w^3 + 2w^2-10w -19,
and the three roots are in very bad form.
Note,when w =2, x= x and y= 16 - 56 + 49 = 9
So, here I only give you one set of solution
x= 4 and y = 9.