If the system of linear equations : l x+y+2 z=6, 2 x+3 y+a z=a+1,… - Vidyadip

MCQ

If the system of linear equations :
$
\begin{array}{l}
x+y+2 z=6, \\
2 x+3 y+a z=a+1, \\
-x-3 y+b z=2 b,
\end{array}
$
where $a , b \in R$, has infinitely many solutions, then $7 a+3 b$ is equal to :

A
9
B
12
✓
16
D
22

✓

Answer

Correct option: C.

16

(C) 16
$
\begin{array}{l}Sol.\
\Delta=\left|\begin{array}{ccc}
1 & 1 & 2 \\
2 & 3 & a \\
-1 & -3 & b
\end{array}\right|=0 \\
\Rightarrow 2 a+b-6=0\qquad\ldots(1) \\
\Delta_1=\left|\begin{array}{ccc}
1 & 1 & 6 \\
2 & 3 & a+1 \\
-1 & -3 & 2 b
\end{array}\right|=0 \\
\Rightarrow a+b-8=0 \qquad\ldots(2)\\
\text { Solving }(1)+(2) \\
a=-2, b=10 \\
\Rightarrow 7 a+3 b=16
\end{array}
$

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