Question

If the system of linear equations
$2x + 2y + 3z = a$
$3x - y + 5z = b$
$x - 3y + 2z = c$
where $a, b, c$ are non-zero real numbers, has more then one solution, then :

• A. $b - c - a = 0$
• B. $a + b + c = 0$
• C. $b + c - a = 0$
• D. $b - c + a = 0$

Answer 1

Answer: (A)

$P_1 : 2x + 2y + 3z = a$
$P_2 : 3x - y + 5z = b$
$P_3 : x - 3y + 2z = c$
We find
$P_1 + P_3 = P_2 \; \Rightarrow \; a + c = b$