Question

The equations

$x + y + z = 6,x + 2y + 3z = 10,x + 2y + mz = n$ give infinite number of values of the triplet (x, y, z) if

• A. $m = 3,n \in R$
• B. $m = 3,n \neq 10$
• C. $m = 3,n = 10$
• D. None of these

Answer 1

Answer: (C)

$m = 3,n = 10$

Answer 2

Each of the first three options contains $m = 3$. When $m = 3$, the last two equations become $x + 2y + 3z = 10$and $x + 2y + 3z = n$.

Obviously, when $n = 10$ these equations become the same. So we are left with only two independent equations to find the values of the three unknowns.

Consequently, there will be infinite solutions.