Question

The ordered pair (a, b), for which the system of linear equations
3x - 2y + z = b
5x - 8y + 9z = 3
2x + y + az = -1
has no solution, is :

• A. $(3,\frac{1}{3})$
• B. $(-3,\frac{1}{3})$
• C. $(-3,-\frac{1}{3})$
• D. $(3,-\frac{1}{3})$

Answer 1

Answer: (C)

$(-3,-\frac{1}{3})$

Answer 2

The correct answer is (C) : $(-3,-\frac{1}{3})$
$\begin{vmatrix} 3 & -2 & 1 \\\ 5 & -8 & 9 \\\ 2 & 1 & \alpha \end{vmatrix} = 0 \Rightarrow -14\alpha - 42 = 0 \Rightarrow \alpha = -3$
Now 3(equation (1)) – (equation (2)) – 2(equation (3)) is
3(3x – 2y + z – b) – (5x – 8y + 9z – 3) – 2(2x + y + az + 1) = 0
⇒ –3b + 3 – 2 = 0
$⇒b=\frac{1}{3}$
So for no solution
$a = –3$ and $b≠\frac{1}{3}$