Question

Resolver el ejercicio con el método de igualación y reducción

Answer 1

Explicación paso a paso:

igualación

$5x - 2y = 2 \\ 5x = 2 + 2y \\ x = \frac{2 + 2y}{5} \\ \\ x + 2y = 2 \\ x = 2 - 2y$

$2 - 2y = \frac{2 + 2y}{5} \\ 10 - 10y = 2 + 2y \\ - 2 + 10 = 2y + 10y \\ 8 = 12y \\ y = \frac{8}{12} = \frac{4}{6} \\ y = \frac{4}{6}$

$x = 2 - 2y \\ = 2 - 2 \times \frac{4}{6} \\ = 2 - \frac{8}{6} = \frac{12}{6} - \frac{8}{6} = \frac{4}{6} \\ x = \frac{4}{6}$

reducción

$5x - 2y = 2 \\ x + 2y = 2 \\ 6x = 4 \\ x = \frac{4}{6} \\ x + 2y = 2 \\ x = 2 - 2y \\ x = 2 - 2 \frac{4}{6} \\ = 2 - \frac{8}{6} = \frac{12}{6} - \frac{8}{6} = \frac{4}{6}$

comprobamos

$5 \times \frac{4}{6} - 2 \times \frac{4}{6} = \frac{20}{6} - \frac{8}{6} = \frac{12}{6} = 2$

$\frac{4}{6} + 2 \times \frac{4}{6} = \frac{4}{6} + \frac{8}{6} = \frac{12}{6} = 2$

espero te sirva

x+2y=2

2y=2-x

y=2-x/2

=2-4/6/2=4/6