Question

For two variables $x$ and $y$ regression equations are given as $7x-3y-18=0$ and $4x-y-11=0$ then what is the arithmetic mean of $x$ is

• A. $1$
• B. $3$
• C. $7$
• D. $0$

Answer 1

The correct option is B $3$

given equations are $7x-3y=18$ ------(1)

and $4x-y=11$ ------(2)

by solving the given equations, we get the arithmetic mean of $x$ and $y$

$3\times eqn\left(2\right)⟹12x-3y=33$ ------(3)

$eqn\left(3\right)-eqn\left(1\right)⟹5x=15$

$⟹x=3$

Therefore, the arithmetic mean of $x$ is $3$.