spain-selectividad 2021 QB.1

spain-selectividad · Other · selectividad__madrid_matematicas-II_extraordinaria 2.5 marks Simultaneous equations
a) ( 0.75 points) Find a single system of two linear equations in the variables $x$ and $y$, which has as solutions $\{ x = 1 , y = 2 \}$ and $\{ x = 0 , y = 0 \}$.
b) (1 point) Find a system of two linear equations in the variables $x , y$ and z whose solutions are, as a function of the parameter $\lambda \in \mathbb { R }$ :
$$\left\{ \begin{array} { l } x = \lambda \\ y = \lambda - 2 \\ z = \lambda - 1 \end{array} \right.$$
c) ( 0.75 points) Find a system of three linear equations with two unknowns, x and y, that has only the solution $x = 1$ and $y = 2$.
a) ( 0.75 points) Find a single system of two linear equations in the variables $x$ and $y$, which has as solutions $\{ x = 1 , y = 2 \}$ and $\{ x = 0 , y = 0 \}$.

b) (1 point) Find a system of two linear equations in the variables $x , y$ and z whose solutions are, as a function of the parameter $\lambda \in \mathbb { R }$ :

$$\left\{ \begin{array} { l } 
x = \lambda \\
y = \lambda - 2 \\
z = \lambda - 1
\end{array} \right.$$

c) ( 0.75 points) Find a system of three linear equations with two unknowns, x and y, that has only the solution $x = 1$ and $y = 2$.