9000023902
Level:
A
Solve the following system and write the solution as the ordered pair
\([x,y]\).
\[\begin{aligned}
2x + y & = 2 & &
\\x + 2y & = 7 & &
\end{aligned}\]
\([-1;4]\)
\([2;-2]\)
\([1;3]\)
\([3;-4]\)
Systems of linear equations and inequalities
9000023903
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
2x + 3y & = -2, & &
\\3x - 2y & = 10. & &
\end{aligned}\]
Find \(5x + y\).
\(8\)
\(- 12\)
\(- 8\)
\(12\)
9000023904
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
4x - 3y & = -3, & &
\\x + 2y & = 13. & &
\end{aligned}\]
Find \(2x - 7y\).
\(- 29\)
\(- 41\)
\(- 11\)
\(31\)
9000023905
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
2x + 5y & = 7, & &
\\ - 4x - 3y & = 7. & &
\end{aligned}\]
In the following list identify a true statement.
\(x^{2} + y^{2} = 25\)
\(x^{2} + y^{2} = 7\)
\(x^{2} - y^{2} = -7\)
\(y^{2} - x^{2} = 7\)
9000023906
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
2x + 3y & = 4, & &
\\4x + 6y & = 9. & &
\end{aligned}\]
In the following list identify a true statement.
The system does not have any solution.
\(x < y\)
\(x > y\)
\(x = y\)
9000023907
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
- x + 2y & = 6, & &
\\2x + 3y & = 2. & &
\end{aligned}\]
In the following list identify a true statement.
\(|x| = |y|\)
\(|x| < |y|\)
\(|x| > |y|\)
The system does not have any solution.
9000022904
Level:
B
Find the values of a real parameter
\(t\) which
ensure that the following system has a unique solution.
\[ \begin{alignedat}{80}
2x & + &y & + &t & = - &2 & & & & & & & &
\\ - 4x & - 2 &y & + &1 & = &0 & & & & & & & &
\\\end{alignedat}\]
\(t\in \emptyset \)
\(t\in \mathbb{R}\)
\(t = 3\)
\(t = 1\)
\(t\in \mathbb{R}\setminus \{3\}\)
9000022905
Level:
B
Find the values of a real parameter
\(t\) which
ensure that the following system has a unique solution.
\[ \begin{alignedat}{80}
tx & + &y & + &3 & = 0 & & & & & &
\\4x & - 2 &y & + &1 & = 0 & & & & & &
\\\end{alignedat}\]
\(t\in \mathbb{R}\setminus \{ - 2\}\)
\(t\in \mathbb{R}\)
\(t = -2\)
\(t\in \emptyset \)
9000022906
Level:
B
Find the values of a real parameter
\(t\)
which ensure that the following system has a unique solution
\([a,b]\) such that
both \(a\)
and \(b\)
are positive real numbers.
\[ \begin{alignedat}{80}
a & - &tb & = - &2 & & & & & &
\\a & + 2 &tb & = &0 & & & & & &
\\\end{alignedat}\]
\(t\in \emptyset \)
\(t\in \mathbb{R}^{+}\)
\(t\in \mathbb{R}^{-}\)
\(t = 0\)
\(t\in \mathbb{R}\)
9000019907
Level:
B
The augmented matrix of a system of three equations with
three unknowns is row equivalent with the following matrix
\(A'\). Find
the solution of the system.
\[
A' = \left(\begin{array}{ccc|c}
1 & 2 & 4 & 0\\
0 & 2 & 7 & 7\\
0 & 0 & 7 & 35
\end{array}\right)
\]
\([8;-14;5]\)
\([-62;21;5]\)
\([8;14;-5]\)
\([-22;-21;5]\)