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 :
Correct Option: 1
Solution:
$P_{1}: 2 x+2 y+3 z=a$
$P_{2}: 3 x-y+5 z=b$
$P_{3}: x-3 y+2 z=c$
We find
$\mathrm{P}_{1}+\mathrm{P}_{3}=\mathrm{P}_{2} \Rightarrow \mathrm{a}+\mathrm{c}=\mathrm{b}$
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