Question

10a + 3b = 20 por reducción: 12a– 4b = 5

Answer 1

Explicación paso a paso:

$10a + 3b = 20 \: \: \: ( \times 4) \\ 12a - 4b = 3 \: \: \: \: \: \: ( \times 5) \\ \\ 40a + 12b = 80 \\ 36a - 12b = 15 \\ 76a = 95 \\ a = \frac{95}{76} = \frac{5}{4}$

$10a + 3b = 20 \\ 10 \times \frac{5}{4} + 3b = 20 \\ \frac{50}{4} + 3b = 20 \\ 3b = 20 - \frac{50}{4 } = \frac{80}{4} - \frac{50}{4} = \frac{30}{4} \\ b = \frac{ \frac{30}{4} }{3} = \frac{30}{4} \times \frac{1}{3} = \frac{30}{12} = \frac{10}{4} \\ b = \frac{10}{4}$

$10 \times \frac{5}{4} + 3 \times \frac{10}{4} = \frac{50}{4} + \frac{30}{4} \\ = \frac{80}{4} = 20 \\ \\ 12 \times \frac{5}{4} - 4 \times \frac{10}{4} = \\ \frac{60}{4} - \frac{40}{4} = \frac{20}{4} = 5$

espero te sirva