Question

Number of solutions for the system of equations $x+2y+z=0,3x+5y+2z=2$ and $2x+4y+2z=1$

• A. $1$
• B. infinity
• C. $2$
• D. $0$

Answer 1

The correct option is D $0$

Consider the first equation
$x+2y+z=0\cdots \left(1\right)$

Consider the last equation
$2x+4y+2z=1$
$\Rightarrow x+2y+z=\frac{1}{2}\cdots \left(2\right)$

Hence both $\left(1\right)$ and $\left(2\right)$ consist of a system of parallel planes.
Therefore, they never intersect and hence they do not have any common solution.