Answer: \(x=6\sqrt7-7\), \(y=6-2\sqrt7\).

Answer: \(x=6\sqrt7-7\), \(y=6-2\sqrt7\).

From the first equation,

\(x=11-3y.\)

Substitute this into \(x-\sqrt7y=7\):

\(11-3y-\sqrt7y=7.\)

So

\((3+\sqrt7)y=4.\)

Hence

\(y=\frac4{3+\sqrt7}.\)

Rationalising the denominator,

\(y=\frac{4(3-\sqrt7)}{9-7}=2(3-\sqrt7)=6-2\sqrt7.\)

Now substitute into \(x=11-3y\):

\(x=11-3(6-2\sqrt7)=6\sqrt7-7.\)