Question

The number of common solutions of $x+2y=8$ and $2x+y=8$ is _____

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

Answer 1

Answer: (B)

$1$

Given, $x+2y=8$
$\Rightarrow x=8-2y$ --- $\left(1\right)$
Substituting $x$ in $2x+y=8$, we get
$2(8-2y)+y=8$
$\Rightarrow 16-4y+y=8$
$\Rightarrow 3y=8$
$\Rightarrow y=\frac{8}{3}$
Substituting in eqn 1 we get
$\Rightarrow x=8-2\left(\frac{8}{3}\right)=\frac{8}{3}$
So, they have one solution.