Use Cramer's rule to find the value of $a$ : $- 4 a - 2 b = - 2$ and $7 a - b = - 1$

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Solution

The correct option is A 0
Given equations are $- 4 a - 2 b = - 2, 7 a - b = - 1$
Using Cramer's rule, find the determinant of the coefficient matrix,
$D = ∣ ∣ ∣ \begin{matrix} - 4 & - 2 7 & - 1 \end{matrix} ∣ ∣ ∣ = - 4 \times - 1 (7 \times - 2)$ $= 4 - 14$ $= - 10$
Similarly, find the determinant of $a$ coefficient matrix,
$D_{a} = ∣ ∣ ∣ \begin{matrix} - 2 & - 2 - 1 & - 1 \end{matrix} ∣ ∣ ∣ = - 2 \times - 1 - (- 1 \times - 2)$ $= 2 - 2 = 0$
Applying Cramer's rule, we have
$a = \frac{D_{a}}{D}$
$∴ a = \frac{0}{- 10} = 0$
Therefore, the value of $a$ is $0$ .

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