9000020904 Level: CDetermine all the values of the parameter c∈R so that the following system has two solutions in R×R. x2+y2=2x+c=y|c|<2|c|=2|c|>2c=2
9000020905 Level: CFind the condition on the parameter c∈R which ensures that the following system has a unique solution in R×R. x2+y2=2x+c=y|c|=2|c|>2|c|<2c=2
9000020906 Level: AIdentify an equation which can be obtained from the following system by eliminating one of the variables. y2−2x+3=0x−y−1=0(y−1)2=0(y+1)2=0(x−4)2=0(x+2)2=0
9000020907 Level: BIdentify a true statement related to the solution of the following system in R×R. 2x2−y2−2x−5=03x−y−5=0The system has no solution.The system has two solutions.The system has a unique solution.None of the above conclusions can be obtained.
9000020903 Level: BIdentify a true statement related to the solution of the following system in R×R. x2+4y2−2x=15x−y+1=0The system has two solutions.The system has a unique solution.The system does not have any solution.The system has infinitely many solutions.
9000020908 Level: CAssuming that the real parameter c satisfies c>16, solve the system and identify a true statement. y2−4x=08x−4y+c=0The system has no solution.The system has two solutions.The system has a unique solution.The system has infinitely many solutions.
9000009909 Level: CConsider the system y=kx,y=a, where a, k are real parameters and x, y are real variables. Determine the conditions for a and k so that the system has a unique solution in R−×R−.a<0 and k>0a<0 and k<0a>0 and k<0a>0 and k>0