Quick help solving this system

[acciogo]

Alright so here is what I have. I have been struggling with this for over an hour, and I finally broke down to see if the Internet can be of any help.


Solve this system:

sqrt(x) + sqrt(y) = 2

x + y = 10

Solve this system. What is the "+" in the first equation was changed to a "-"?


I am also provided with a hint: "There is a solution in one case and no solution in another. Solve for sqrt(y) in the first equation. Substitute into equation 2... It may help to let u = sqrt(y)."

I did some research and I think it has something to do with u-substitution. But I don't remember anything about u-substitution, so I am at a loss of what to do. Any help you can provide would be greatly appreciated. Thanks in advance!

 

[Deleted member 4993]

Alright so here is what I have. I have been struggling with this for over an hour, and I finally broke down to see if the Internet can be of any help.


Solve this system:

sqrt(x) + sqrt(y) = 2

x + y = 10

Solve this system. What is the "+" in the first equation was changed to a "-"?


I am also provided with a hint: "There is a solution in one case and no solution in another. Solve for sqrt(y) in the first equation. Substitute into equation 2... It may help to let u = sqrt(y)."

I did some research and I think it has something to do with u-substitution. But I don't remember anything about u-substitution, so I am at a loss of what to do. Any help you can provide would be greatly appreciated. Thanks in advance!

"square" the first equation.

That gives you:

x + y + 2*√(x*y) = 4.................................(3)

subtract (2) from (3)

2*√(x*y) = -6

Now continue.....