1. Solve the simultancous equations \[ \begin{aligned} 2 y^{2}+x^{2}=-6 x+42 \\ 2 x+y=-3\end{aligned} \] Show clear algebraic working.

Question 5 - of 19 step 1 of 1 \( z \) varies directly as the cube of \( x \) and inversely as \( y \). If \( z=237 \) when \( x=10 \) and \( y=2 \), find \( z \) if \( x=8 \) and \( y=3 \). Round your answer to two decimal places if necessary.

26. Resolva as equaçös. a) \( (x+1)^{2}=7+x \) b) \( (x-2)^{2}-x=1 \) c) \( x^{2}=\frac{4}{5} x+\frac{1}{5} \) d) \( \frac{x^{2}}{4}-\frac{x}{3}+\frac{1}{9}=0 \) e) \( x^{2}-3=\frac{x-3}{6} \) f) \( \frac{x^{2}-5 x}{6}+1=\frac{2 x+11}{3} \)

2 varies directly as the cube of \( x \) and inversely as \( y \). If \( z=237 \) when \( x=10 \) and \( y=2 \), find \( z \) if \( x=8 \) and Round your answer to two decimal places if necessary.

\( 2 x - \frac { 16 x + 1 } { 5 ^ { x + 1 } } + 1 = 0 \)

Determine the implied domain of the following function. Express your answer in interval notation. \[ g(x)=-3 x+2 \] \[ \]