If system of linear equations 2x + 2y + 3z = a ; 3x - y + 5z = b ; x - 3y + 2z = c Where a, b, c are

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3 and 4 .Determinants and Matrices

hard

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 than one solution, then

A

$b \,-\, c \,+\, a = 0$

B

$b\, -\, c\, -\,a = 0$

C

$a \,+\, b\, +\, c = 0$

D

$b \,+ \,c\, -\,a = 0$

(JEE MAIN-2019)

Solution

$2x+2y+3z=a$ $(1)$

$3x-y+5z=b$ $(2)$

$x-3y+2z=c$ $(3)$

$(2x+2y+3z)+(x-3y+2z)-(3x-y+5z)=0$

$ \Rightarrow $ $a+c-b=0$

Standard 12

Mathematics

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