C

9000031110

Level: 
C
Solve the following system of equations and identify a correct statement. \[\begin{aligned} \left |x - 2\right | & = y & & \\\left |y + 2\right | & = x - 6 & & \end{aligned}\]
The system has no solution.
The system has a unique solution.
The system has two solutions.
The system has more than two solutions.

9000031108

Level: 
C
Solve the following system of equations and identify a correct statement. \[\begin{aligned} 2x^{2} - y = 2 & & \\\left |x\right | + y = 1 & & \end{aligned}\]
The system has two solutions.
The system does not have any solution.
The system has a unique solution.
The system has more than two solutions.

9000031109

Level: 
C
Solve the following system of equations and identify a correct statement. \[\begin{aligned} \left |x\right | = x + y & & \\\left |y\right | = 1 + x & & \end{aligned}\]
The system has a unique solution.
The system does not have any solution.
The system has two solutions.
The system has more than two solutions.

9000031106

Level: 
C
Solve the following system of equations and identify a correct statement. \[\begin{aligned} \sqrt{x + y} & = \left |x\right | & & \\x + y & = 4 & & \end{aligned}\]
The system has two solutions \(\left [x_{1},y_{1}\right ]\), \(\left [x_{2},y_{2}\right ]\), where \(x_{1} = -x_{2}\).
The system does not have any solution.
The system has a unique solution.
The system has two solutions \(\left [x_{1},y_{1}\right ]\), \(\left [x_{2},y_{2}\right ]\), where \(x_{1} = x_{2}\).

9000031107

Level: 
C
Solve the following system of equations and identify a correct statement. \[\begin{aligned} \sqrt{x} = y & & \\x^{2} + y^{2} = 6 & & \end{aligned}\]
The system has a unique solution.
The system does not have any solution.
The system has two solutions.
The system has more than two solutions.

9000028410

Level: 
C
Find the condition which is equivalent to the fact that the equation \(ax^{2} + bx + c = 0\) with \(x\in \mathbb{R}\) and real coefficients \(a\), \(b\), \(c\) has two solutions and one of the solutions is a reciprocal value of the second solution.
\(b^{2} - 4ac > 0\text{ and }\frac{c} {a} = 1\)
\(b^{2} - 4ac > 0\text{ and }a = c\)
\(b^{2} - 4ac > 0\text{ and }\frac{c} {a} = -1\)
\(b^{2} - 4ac > 0\text{ and }a = -c\)