The values of a and b, for which the system of equations
Question:

The values of $a$ and $b$, for which the system of equations

$2 x+3 y+6 z=8$

$x+2 y+a z=5$

$3 x+5 y+9 z=b$

has no solution, are :

  1. $a=3, b \neq 13$

  2. $a \neq 3, b \neq 13$

  3. $a \neq 3, b=3$

  4. $a=3, b=13$


Correct Option: 1

Solution:

$D=\left|\begin{array}{lll}2 & 3 & 6 \\ 1 & 2 & a \\ 3 & 5 & 9\end{array}\right|=3-a$

$D=\left|\begin{array}{lll}2 & 3 & 8 \\ 1 & 2 & 5 \\ 3 & 5 & b\end{array}\right|=b-13$

If $a=3, b \neq 13$, no solution.

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