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 :

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

Tardigrade Admin · Accepted Answer

P1: 2x + 2y + 3z = a P2: 3x - y + 5z = b P3: x - 3y + 2z = c We find P1 + P3 = P2 ⇒ a + c = b

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

$b - c - a = 0$

$a + b + c = 0$

$b + c - a = 0$

$b - c + a = 0$

$P_{1} : 2 x + 2 y + 3 z = a$
$P_{2} : 3 x - y + 5 z = b$
$P_{3} : x - 3 y + 2 z = c$
We find
$P_{1} + P_{3} = P_{2} \Rightarrow a + c = b$

Q. 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 :

b−c−a=0

a+b+c=0

b+c−a=0

b−c+a=0