Solve the following equation by cramer's method:
$7 x + 3 y = 15, 12 y - 5 x = 39$

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Solution

$7 x + 3 y = 15; 12 y - 5 x = 39$

$D = ∣ ∣ ∣ \begin{matrix} 7 & 3 - 5 & 12 \end{matrix} ∣ ∣ ∣ = 7 \times 12 - (- 5) \times 3 = 84 + 15 = 99$

$D_{x} = ∣ ∣ ∣ \begin{matrix} 15 & 3 39 & 12 \end{matrix} ∣ ∣ ∣ = 15 \times 12 - 39 \times 3 = 180 - 117 = 63$

$D_{y} = ∣ ∣ ∣ \begin{matrix} 7 & 15 - 5 & 39 \end{matrix} ∣ ∣ ∣ = 7 \times 39 - (- 5) \times 15 = 273 + 75 = 348$

$x = \frac{D_{x}}{D} = \frac{63}{99} = \frac{7}{11}$

$y = \frac{D_{y}}{D} = \frac{348}{99} = \frac{116}{33}$

$(x, y) = (\frac{7}{11}, \frac{116}{33})$

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