4) Discutere e risolvere il seguente sistema lineare al variare del parametro \( k \in \mathbb{R} \) : \[ \begin{array}{l}k x+y+z=1 \\ x+k y+z=1 \\ x+y+k z=1\end{array} \]

\( 1<\quad \begin{array}{r}\text { Determine whether the ordered pair }(4,5) \text { is a solution of the system. } \\ \begin{array}{r}3 x+2 y=2 \\ 2 x+y=3\end{array}\end{array} \)

Evaluating functions: Linear and quadratic or cubic The functions \( f \) and \( g \) are defined as follows. \( f(x)=3 x^{3}+5 \quad g(x)=-5 x+4 \) Find \( f(-2) \) and \( g(7) \). \[ f(-2)=\square \] \( g(7)=\square \)

The cost price of a pen is Rs \( (3 x+5) \) and is selling price is \( \operatorname{Rs}(4 x+3) \) Write the formulato find protit.

\( 1 \leftarrow \quad \begin{array}{l}\text { Solve the system of equations by the substitution method. } \\ \begin{aligned} 4 x+2 y & =-154 \\ x-5 y & =0\end{aligned}\end{array} \)

O Functions and Lines Evaluating functions: Linear and quadratic or cubic The functions \( f \) and \( g \) are defined as follows. \[ f(x)=-2 x^{2}-3 \quad g(x)=3 x-1 \] Find \( f(5) \) and \( g(-2) \). Simplify your answers as much as possible. \[ f(5)=\square \] \( g(-2)=\square \)