Solve the system of linear equation $3 x - 2 y = 13$ and $4 x + y = 21$

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Solution

$a_{1} = 3, a_{2} = 4, b_{1} = - 2, b_{2} = 1, c_{1} = 13, c_{2} = 21$

$x = \frac{c_{1} b_{2} - c_{2} b_{1}}{a_{1} b_{2} - a_{2} b_{1}} = \frac{13 * 1 + 21 * 2}{3 * 1 + 8} = \frac{55}{11} = 5$

$y = \frac{c_{2} a_{1} - c_{1} a_{2}}{a_{1} b_{2} - a_{2} b_{1}} = \frac{21 * 3 - 13 * 4}{3 * 1 + 8} = \frac{11}{11} = 1$

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