Question

The system of equations $x+2y=11-2x-4y=22$ has

• A. only one solution
• B. finitely many solutions
• C. no solution
• D. infinitely many solutions

Answer 1

Answer: (C)

Let $A=\left[\begin{array}{cc}1& 2\\ -2& -4\end{array}\right]$
Since $|A|=-4+4=0$, and $2\left(x+2y\right)=22$
i.e., $2x+4y=22$ and $2x+4y=-22$
$\therefore$ the given equation has no solution.