Question

√X + Y = 7
X + √Y = 11

find x and y!

Answer 1

x-y = 7
y = 2

Answer 2

Haha! Nop! Wrong! (:

Answer 3

are both positive?

Answer 4

there are 2 solutions, one of them would be x=8.51253 and y=6.1875

Answer 5

You want the solutions to the two equations?

Answer 6

https://www.desmos.com/calculator

Answer 7

The solutions are very easy to find with hit and trial. But I am sure he needs the method. Using a calculator is cheating here!

Answer 8

The solutions are easy its X=9 and Y=4! :D
What is the method here?
@greenlegodude57 @AkashdeepDeb

Answer 9

From the first equation,
\[\sqrt x+y=7~~\iff~~\sqrt x=7-y~~\Rightarrow~~x=(7-y)^2\]
Substitute into the second equation:
\[(7-y)^2+\sqrt y=11\]
Expand and simplify:
\[\begin{align*}49-14y+y^2+\sqrt y&=11\\
\sqrt y&=-y^2+14y-38\\
y&=\left(y^2-14y+38\right)^2\\
0&=y^4-28y^3+272y^2-1065y+1444
\end{align*}\]
\(y=4\) is a root, but how to get that manually? Maybe try the rational root theorem, or guess and check, noting that \(x,y>0\) must hold.