Answer: The answer are (a) (2, 2) and (d) (-2, -2).
Step-by-step explanation: The given system of equations is
\(x^2+y^2=8,~~~~~~~~~~~~(A)\\\\x-y=0.~~~~~~~~~~~~~~~(B)\)
We are to select all the correct options from the given that are solutions to the above system.
Let us solve the system of equations as follows:
From equation (B), we have
\(x-y=0\\\\\Rightarrow x=y.~~~~~~~~~~~(C)\)
Using equation (C) in equation (B), we have
\(x^2+y^2=8\\\\\Rightarrow x^2+x^2=8\\\\\Rightarrow2x^2=8\\\\\Rightarrow x^2=4\\\\\Rightarrow x=\pm2,\)
and from (C) again, we get
\(y(x=2)=2,\\\\y(x=-2)=-2.\)
Therefore, the solutions are (2, 2) and (-2, -2).
Thus, (a) and (d) are the correct options.
