A

2010006502

Level: 
A
Identify which of the following systems of equations has infinitely many solutions.
\( \begin{aligned} \frac12x-3y&=12\\ -\frac{1}3x+2y&=-8 \end{aligned} \)
\( \begin{aligned} \frac13 x-2y&=12 \\ -\frac12 x+3y&=-16 \end{aligned} \)
\( \begin{aligned} \frac12 x+2y&=12 \\ -\frac13 x-3y&=-12 \end{aligned} \)
\( \begin{aligned} \frac12 x-y&=12 \\ -\frac23 x+4y&=-8\end{aligned} \)

2010006501

Level: 
A
In \( \mathbb{R}\times\mathbb{R} \), find the solution set of the equation: \[ 3y-\frac{x+y}2=1-\frac43x \]
\( \left\{ \left[-3y+\frac65;y\right],\ y\in\mathbb{R}\right \} \)
\( \left\{ \left[-3y+\frac65;x+\frac13\right],\ x\in\mathbb{R},y\in\mathbb{R}\right \} \)
\( \left\{ \left[\frac13 y+\frac65;y\right],\ y\in\mathbb{R}\right \} \)
\( \emptyset \)

2010006103

Level: 
A
The light travels at speed of \(300\, 000\) kilometers per second. How many kilometres it travels in \(24\) hours? Give the result in exponential notation.
\( 2.592\cdot10^{10}\,\mathrm{km} \)
\( 2.592\cdot10^{11}\,\mathrm{km} \)
\( 25.92\cdot10^{10}\,\mathrm{km} \)
\( 2.592\cdot10^{9}\,\mathrm{km} \)