A

2000020406

Level: 
A
Let's denote by \(M\) the set of all points in the plane such that their coordinates \(\left[x;y\right]\) satisfy the relation \(2x-y+1=0\). Then, choose the true statement about \(M\).
\(M\) is a line.
\(M\) is a ray.
\(M\) is a finite set of point.
\(M\) is a half plane.

2000020403

Level: 
A
In a system of two linear equations with two unknowns, the assignment of the second equation is inadvertently blurred, but we know that the first component of the solution of the system is \(x=-1\). We do not know the value of \(y\), but the part of the figure illustrating the graphical solution is preserved. The first equation is \(x-y+2=0\). Determine the second (blurred) equation of this system.
\(7x-11y+18=0\)
\(x-y+2=0\)
\(7x+11y-18=0\)
\(x+y+2=0\)

2000020401

Level: 
A
The system of two linear equations can be represented graphically by two lines. Decide which of the systems given below corresponds to the following picture.
\[\begin{aligned} x-y&=-4\\ x+\frac53y&=-\frac43\\ \end{aligned}\]
\[\begin{aligned} x-y&=-4\\ \frac13x+\frac53y&=-\frac43\\ \end{aligned}\]
\[\begin{aligned} x+y&=-4\\ x+\frac53y&=-\frac43\\ \end{aligned}\]
\[\begin{aligned} x-y&=-4\\ 3x+5y&=-\frac43\\ \end{aligned}\]

2000020307

Level: 
A
Describe the set of all ordered pairs of real numbers in the form \([x;y]\) that are solutions to the followig equation. \[ \frac{x-7}{y+1}=5 \] Which of the descriptions of our solution set is correct?
\[ \left\{ \left[5m+12;m\right];m\in\mathbb{R}\setminus \left\{-1\right\}\right\} \]
\[ \left\{ \left[x;0.2x-2.4\right];x\in\mathbb{R}\setminus \left\{-0.7\right\}\right\} \]
\[ \left\{ \left[5a-12;a\right];a\in\mathbb{R}\setminus \left\{-1\right\}\right\} \]
\[ \left\{ \left[q;0.2q+2.4\right];q\in\mathbb{R}\setminus \left\{-1.8\right\}\right\} \]

2000020305

Level: 
A
Describe the set of all ordered pairs of real numbers in the form \(\left[x;y\right] \) that are solutions to the following equation. \[\frac{y+2}{x-4}=3\] Which of the descriptions of our solution set is incorrect?
\[ \left\{ \left[2b;b+\frac{14}{3}\right];b\in\mathbb{R}\setminus \left\{2\right\}\right\} \]
\[ \left\{ \left[x;3x-14\right];x\in\mathbb{R}\setminus \left\{4\right\}\right\} \]
\[ \left\{ \left[\frac{y+14}{3};y\right];y\in\mathbb{R}\setminus \left\{-2\right\}\right\} \]
\[ \left\{ \left[\frac{a}{3};a-14\right];a\in\mathbb{R}\setminus \left\{12\right\}\right\} \]

2000020303

Level: 
A
Solve the given system of equations in the set of real numbers. \[\begin{aligned} x+y&=4+\frac{1}{27}\\ x\cdot y&=\frac{4}{27}\\ \end{aligned}\] In the following list identify a true statement.
\(|x-y|=\frac{107}{27}\)
The system has exactly one solution.
The system has no solution.
The system has infinitely many solutions.