5. The numbers $x$ and $y$ are solutions to the system of equations param 1, where $a$ is a parameter. What param 2 value does the expression param 3 take?

| param1 | param2 | param3 |  |
| :---: | :---: | :---: | :---: |
| $\left\{\begin{array}{l}a x+y=a+1 \\ x+4 a y=3\end{array}\right.$ | maximum | $x^{2}-6 y^{2}$ |  |
| $\left\{\begin{array}{l}-x+a y=2 a \\ a x-y=3 a-5\end{array}\right.$ | minimum | $x^{2}+y^{2}$ |  |
| $\left\{\begin{array}{l}a x+9 y=a+3 \\ x+a y=2\end{array}\right.$ | maximum | $3 y^{2}-x^{2}$ |  |
| $\left\{\begin{array}{l}x+a y=3 a \\ a x+y=a+4\end{array}\right.$ | minimum | $2 x^{2}+y^{2}$ |  |
5. The numbers $x$ and $y$ are solutions to the system of equations param 1, where $a$ is a parameter. What param 2 value does the expression param 3 take?

| param1 | param2 | param3 | Answer |
| :---: | :---: | :---: | :---: |
| $\left\{\begin{array}{l}a x+y=a+1 \\ x+4 a y=3\end{array}\right.$ | maximum | $x^{2}-6 y^{2}$ | 27 |
| $\left\{\begin{array}{l}-x+a y=2 a \\ a x-y=3 a-5\end{array}\right.$ | minimum | $x^{2}+y^{2}$ | 2 |
| $\left\{\begin{array}{l}a x+9 y=a+3 \\ x+a y=2\end{array}\right.$ | maximum | $3 y^{2}-x^{2}$ | 2 |
| $\left\{\begin{array}{l}x+a y=3 a \\ a x+y=a+4\end{array}\right.$ | minimum | $2 x^{2}+y^{2}$ | 6 |