Solve the following simultaneous equations using Cramer's rule.
$3 x + 2 y + 11 = 0; 7 x - 4 y = 9$

x = - 1, y = - 4

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x = 1, y = 6

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x = 1, y = - 9

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x = - 1, y = 3

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Solution

The correct option is D $x = - 1, y = - 4$
Given equations are $3 x + 2 y + 11 = 0$ and $7 x - 4 y = 9$

$⟹ 3 x + 2 y = - 11$ and $7 x - 4 y = 9$

By Cramer's rule,

$D = ∣ ∣ ∣ \begin{matrix} 3 & 2 7 & - 4 \end{matrix} ∣ ∣ ∣ = - 12 - 14 = - 26$

$D_{x} = ∣ ∣ ∣ \begin{matrix} - 11 & 2 9 & - 4 \end{matrix} ∣ ∣ ∣ = 44 - 18 = 26$

$D_{y} = ∣ ∣ ∣ \begin{matrix} 3 & - 11 7 & 9 \end{matrix} ∣ ∣ ∣ = 27 + 77 = 104$

Now, $x = \frac{D_{x}}{D} = \frac{26}{- 26} = - 1$

$y = \frac{D_{y}}{D} = \frac{104}{- 26} = - 4$

Hence, $x = - 1, y = - 4$ .

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