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.
\[ \begin{alignedat}{80}
tx & + &y & + &3 & = 0 & & & & & &
\\4x & - 2 &y & + &1 & = 0 & & & & & &
\\\end{alignedat}\]
\(t\in \mathbb{R}\setminus \{ - 2\}\)
\(t\in \mathbb{R}\)
\(t = -2\)
\(t\in \emptyset \)
9000021801
Level:
C
Solve the following system of inequalities.
\[\begin{aligned}
\frac{1}
{3}(2x + 5) &\geq 0.5\left (\frac{2 + 3x}
{2} + 2\right ) & &
\\0.2(3 - 2x) &\leq \frac{1}
{3}\left (\frac{4 - 2x}
{5} + 2\right ) & &
\end{aligned}\]
\(x\in \left [ -\frac{5}
{4};2\right ] \)
\(x\in [ 2;\infty )\)
\(x\in \left (-\infty ;-\frac{5}
{4}\right ] \)
\(x\in \emptyset \)
9000021802
Level:
C
Solve the following system of inequalities.
\[\begin{aligned}
15x - 2 &\geq 3x + 2 > 2x + 1 & &
\\10x + 1 & > 5x + 1\geq 6 - x & &
\end{aligned}\]
\(x\in \left [ \frac{5}
{6};\infty \right )\)
\(x\in [ - 1;\infty )\)
\(x\in \emptyset \)
\(x\in [ 2;\infty )\)