VII. Find the solution(s) of the following system. \[ \left\{\begin{array}{r}x_{1}+x_{2}+x_{3}+x_{4}=0 \\ 2 x_{1}+2 x_{2}+3 x_{3}+4 x_{4}=0 \\ 2 x_{1}+2 x_{2}+2 x_{3}+2 x_{4}=0 \\ 3 x_{1}+3 x_{2}+4 x_{3}+5 x_{4}=0\end{array}\right. \]

Si \( a = 4 \), ¿cuál es el valor de \( a^2 \)?

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

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

6. Simplify these expressions and find then values if \( x=3, p=-1,4=-2 \) (i) \( 3 p+4+2 q+1 \) (ii) \( 8-6 x+4 x+3 \)

(iii) \( -2 p^{3}-3 p^{2}+4 p+7 \)