Question

The equations $x+2y+z=0,2x+4y+2z=1$ have$\cdots \cdots$ solutions

• A. 0
• B. 1
• C. 8
• D. Infinity

Answer 1

The correct option is A 0

Consider the first equation
$x+2y+z=0$ ...(i)
Consider the second equation
$2x+4y+2z=1$
$\Rightarrow x+2y+z=\frac{1}{2}$ ...(ii)
Hence both i and ii consist of a system of parallel planes.
Therefore they never intersect and hence do not have any solution.