VI. Find the solution(s) of the following system. \[ \begin{array}{r}x+y+z=1 \\ 2 x+3 y+3 z=2 \\ x+2 y+2 z=1\end{array} \] (Write the answer for the questions on your answer sheet. 10 points)

1) \( (0,1)^{2 x}=10 \)

b. प्रमाणित गर्नुहोस (Prove that): \( \frac{1}{1-\mathrm{x}^{\mathrm{a}-\mathrm{b}}}+\frac{1}{1-\mathrm{x}^{\mathrm{b}-\mathrm{n}}}=1 \)

Exercise 3.17 Determine if each one of the following system of linear equations has unique solution, no solution or infinitely many solutions. \( \begin{array}{ccc}x-y=1 & \text { b. } \begin{array}{c}x+y=1 \\ 2 x+3 y=4\end{array} & \begin{array}{c}x-2 y=1 \\ x+y=5\end{array} \\ \begin{array}{l}\text { a. } \\ x+4 y=2\end{array}\end{array} \)

Solve the exponential equation: \( 3^{2x} = 81 \)

\( f(x)=\frac{x+k}{x-1} \) and \( (5,2) \in f^{-1} \), then \( K= \)