B

9000021801

Level: 
B
Solve the following system of inequalities. \[\begin{aligned} \frac{1} {3}(2x + 5) &\geq 0.5\left (\frac{2 + 3x} {2} + 2\right ) & & \\0.2(3 - 2x) &\leq \frac{1} {3}\left (\frac{4 - 2x} {5} + 2\right ) & & \end{aligned}\]
\(x\in \left [ -\frac{5} {4};2\right ] \)
\(x\in [ 2;\infty )\)
\(x\in \left (-\infty ;-\frac{5} {4}\right ] \)
\(x\in \emptyset \)

9000020907

Level: 
B
Identify a true statement related to the solution of the following system in \(\mathbb{R}\times \mathbb{R}\). \[ \begin{alignedat}{80} &2x^{2} & - & &y^{2} & - &2 &x & - 5 & = 0 & & & & & & & & & & \\ & & & &3x & - & &y & - 5 & = 0 & & & & & & & & & & \\\end{alignedat}\]
The system has no solution.
The system has two solutions.
The system has a unique solution.
None of the above conclusions can be obtained.

9000020903

Level: 
B
Identify a true statement related to the solution of the following system in \(\mathbb{R}\times \mathbb{R}\). \[ \begin{alignedat}{80} &x^{2} & + &4 & &y^{2} & - & &2x & = &15 & & & & & & & & & & & & \\ &x & - & & &y & + & &1 & = &0 & & & & & & & & & & & & \\\end{alignedat}\]
The system has two solutions.
The system has a unique solution.
The system does not have any solution.
The system has infinitely many solutions.

9000020901

Level: 
B
The solution of the given set of equations can be interpreted as the intersection of the curves shown in the figure. Find the solution of the system in \(\mathbb{R}\times \mathbb{R}\). \[ \begin{alignedat}{80} &2x^{2} & - &3y &^{2} & = 2 &4 & & & & & & & & \\ &2x & - &3y & & = &0 & & & & & & & & \\\end{alignedat}\]
\([-6;-4],\ [6;4]\)
\([-6;-4]\)
\([6;4]\)
no solution