Question

Resuelvo por sustitución y por igualación.

Answer 1

Explicación paso a paso:

$4x + 6y = 2 \\ 4x = 2 - 6y \\ x = \frac{2 - 6y}{4} \\ \\ 6x + 5y = 1 \\ 6x = 1 - 5y \\ x = \frac{1 - 5y}{6}$

$\frac{1 - 5y}{6} = \frac{2 - 6y}{4} \\ 4 - 20y = 12 - 36y \\ - 12 + 4 = - 36y + 20y \\ - 8 = - 16y \\ 16y = 8 \\ y = \frac{8}{16} = \frac{1}{2} \\ y = \frac{1}{2}$

$x = \frac{1 - 5y}{6} = \frac{1 - 5 \times \frac{1}{2} }{6} = \frac{ \frac{2}{2} - \frac{5}{2} }{6} = \\ = \frac{ - 3}{2} \times \frac{1}{6} = \frac{ - 3}{12} = \frac{ - 1}{4} \\ x = \frac{ - 1}{4}$

2 reducción

$4x + 6y = 2 \\ 4x = 2 - 6y \\ x = \frac{2 - 6y}{4} \\ \\ 6x + 5y = 1 \\ 6 \times ( \frac{2 - 6y}{4} ) + 5y = 1 \\ \frac{12 - 36y}{4} + \frac{20y}{4} = \frac{4}{4} \\ 12 - 36y + 20y = 4$

$- 16y = 4 - 12 \\ - 16y = - 8 \\ 16y = 8 \\ y = \frac{8}{16} = \frac{1}{2}$

comprobamos

$4 \times \frac{ - 1}{2} + 6 \times \frac{1}{2} = \frac{ - 2}{2} + \frac{6}{2} = \frac{4}{2} = 2$

$6 \times \frac{ - 1}{2} + 5 \times \frac{1}{2} = \\ \frac{ - 6}{4} + \frac{5}{2} = \frac{ - 3}{2} + \frac{5}{2 } \\ = \frac{2}{2} = 1$

espero te sirva