Question

Consider the system of linear equations$\begin{cases}x + y + t = 4, \\\2x - 4t = 7, \\\x + y + z = 5, \\\x - 3y - z - 10t = \lambda,\end{cases}$where $x, y, z, t$ are variables and $\lambda$ is a constant. Then which one of the following is true?

• A. If $\lambda = 1$, then the system has a unique solution.
• B. If $\lambda = 2$, then the system has infinitely many solutions.
• C. If $\lambda = 1$, then the system has infinitely many solutions.
• D. If $\lambda = 2$, then the system has a unique solution.

Answer 1

Answer: (C)

If $\lambda = 1$, then the system has infinitely many solutions.

Answer 2

The correct option is (C): If $\lambda = 1$, then the system has infinitely many solutions.