A

1003083003

Level: 
A
Find the solution set of the following system of equations. \[ \begin{aligned}\frac23 x-\frac12y&=1 \\ -2x+\frac32y&=-3 \end{aligned} \]
\( \left\{\left[x; \frac{4x-6}3\right]\colon x\in\mathbb{R}\right\} \)
\( \left\{\left[x; y\right]\colon x\in\mathbb{R}\text{, } y\in\mathbb{R}\right\} \)
\( \emptyset \)
\( \left\{[0; -2]\right\} \)

1003083002

Level: 
A
Identify which of the sets is not the solution set of the following system of equations. \[ \begin{aligned} \frac12 x-y&=3 \\ \frac x3 - \frac23 y &=2 \end{aligned} \]
\( \left\{\left[6+2y;\frac{x-6}2\right]\colon x\in\mathbb{R}\text{, }y\in\mathbb{R}\right\} \)
\( \left\{\left[x; \frac{x-6}2\right]\colon x\in\mathbb{R}\right\} \)
\( \left\{\left[6+2y;y\right]\colon y\in\mathbb{R}\right\} \)
\( \left\{\left[2t;t-3\right]\colon t\in\mathbb{R}\right\} \)

1003083001

Level: 
A
Identify which of the following systems of equations has infinitely many solutions.
\( \begin{aligned} \frac13x-4y&=2\\ -\frac{x}4+3y&=-\frac32 \end{aligned} \)
\( \begin{aligned} \frac13 x-4y&=2 \\ -x+12y&=6 \end{aligned} \)
\( \begin{aligned} \frac13 x-4y&=2 \\ \frac x4-6y&=6 \end{aligned} \)
\( \begin{aligned} \frac13 x-4y&=2 \\ \frac x3-4y&=0 \end{aligned} \)

1003102503

Level: 
A
Find the complex roots of the following quadratic equation. \[ 5x^2 + 12 = 0 \]
\( x_1=-\frac{2\sqrt{15}}5\mathrm{i}\text{, }x_2=\frac{2\sqrt{15}}5\mathrm{i} \)
\( x_1=-\frac{\sqrt{15}}5\mathrm{i}\text{, }x_2=\frac{\sqrt{15}}5\mathrm{i} \)
\( x_1=-\frac{\sqrt{12}}5\mathrm{i}\text{, }x_2=\frac{\sqrt{12}}5\mathrm{i} \)
\( x_1=-\frac{2\sqrt{3}}5\mathrm{i}\text{, }x_2=\frac{2\sqrt{3}}5\mathrm{i} \)