9000023904
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
4x - 3y & = -3, & &
\\x + 2y & = 13. & &
\end{aligned}\]
Find \(2x - 7y\).
\(- 29\)
\(- 41\)
\(- 11\)
\(31\)
Systems of linear equations and inequalities
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.
9000023908
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
2x - y & = -1, & &
\\4x - y & = 1. & &
\end{aligned}\]
In the following list identify a true statement.
\(y\) is
a prime number.
\(x\) is
a prime number.
\(x + y\) is
a prime number.
\(x - y\) is
a prime number.
9000023909
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
2x + 3y & = 0, & &
\\3x + 2y & = 5. & &
\end{aligned}\]
In the following list identify a true statement.
\(- 3\leq y\leq - 1\)
\(- 1\leq x\leq 2\)
\(- 2\leq x\leq 2\)
\(2\leq y\leq 4\)
9000023910
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
3x - y & = 1, & &
\\2x - y & = -1. & &
\end{aligned}\]
In the following list identify a true statement.
\(x\)
divides \(6\).
\(x\)
divides \(3\).
\(y\)
divides \(4\).
\(y\)
divides \(6\).
1003034503
Level:
B
Students registered for sports camps. For the biking camp registered by \( 18 \) students more than for the boating camp. After some time one of the students switched his registration from the boating camp to the biking camp. Now, there is two times more bikers than boaters. How many students registered originally for the boating camp?
\( 21 \)
\( 39 \)
\( 20 \)
\( 15 \)
1003034504
Level:
B
A double-digit number equals to the four multiple of its digit sum. Determine the digit in the unit position if you know that the digit of tens is by \( 4 \) lower than the digit of units.
\( 8 \)
\( 4 \)
\( 6 \)
\( 0 \)
1003034505
Level:
B
The March price of a T-shirt and shorts was \( 600\,\mathrm{CZK} \) together. In April there was on store price adjustment. The price of the shorts decreased by \( 10\% \) and the price of the T-shirt increased by \( 10\% \). So the April price of both together the shorts and the T-shirt was by \( 20\,\mathrm{CZK} \) lower. What was the April price of the T-shirt?
\( 220\,\mathrm{CZK} \)
\( 200\,\mathrm{CZK} \)
\( 180\,\mathrm{CZK} \)
\( 400\,\mathrm{CZK} \)