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

x = 3, y = 2

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x = 4, y = 5

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x = 5, y = 8

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x = 4, y = 4

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Solution

The correct option is A $x = 3, y = 2$
Given, $3 x - y = 7$ and $x + 4 y = 11$
$D = ∣ ∣ ∣ \begin{matrix} 3 & - 1 1 & 4 \end{matrix} ∣ ∣ ∣ = 12 + 1 = 13 D_{x} = ∣ ∣ ∣ \begin{matrix} 7 & - 1 11 & 4 \end{matrix} ∣ ∣ ∣ = 28 + 11 = 39 D_{y} = ∣ ∣ ∣ \begin{matrix} 3 & 7 1 & 11 \end{matrix} ∣ ∣ ∣ = 33 - 7 = 26 ∴ x = \frac{D_{x}}{D} = \frac{39}{13} = 3 ∴ y = \frac{D_{y}}{D} = \frac{26}{13} = 2$
The values are $x = 3$ and $y = 2$ .

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