Given the system of equations: \( \left\{\begin{array}{l}x+y+z=1 \\ y-3 z=-6 \\ 2 x+y+5 z=9\end{array}\right. \) (a) Determine the type of system: inconsistent dependent (b) If your answer is dependent, find the complete solution. Write \( x, y \), and \( z \) as functions of \( t \), where \( z=t \). If your answer is inconsistent, write DNE in the box for all three variables. \( x=\square \) \( y=\square \)

ii) \( \frac{4 x^{2}+3 x+7}{x+1} \)

5. Separen en términos y resuelvan. a. \( \left(-\frac{4}{3}+\frac{1}{6}\right)-\left(-\frac{3}{2}\right)^{-2}+\sqrt[3]{\left(\frac{3}{4}+\frac{1}{8}\right)-} \) b. \( \left(\frac{3}{2}-\frac{1}{2}\right)^{2}+\sqrt[3]{-\frac{1}{64}}-0.5= \) c. \( \sqrt[3]{1-\frac{7}{8}}-\left(-\frac{2}{5}+\frac{1}{10}\right)^{-4}+0.3- \) d. \( -\left(\frac{8}{5}-\frac{6}{15}\right)-\sqrt[3]{1-\frac{31}{32}}+\left(\frac{7}{5}\right)^{2}= \)

\( x = \frac { - ( - 1 ) \pm \sqrt { - 79 } } { 2.1 } \)

d the exact value of the solution to the equation \( 2 e^{2 x}-7 e^{x}-4=0 \)

2.3 Express \( \frac{1}{\sqrt{2}+1} \) in its simpl