Question

solución a la ecuación 4x+2y=31/6. 6x-y=43/4​

Answer 1

Explicación paso a paso:

$4x + 2y = \frac{31}{6} \\ \frac{4x}{1} \times \frac{6}{6} = \frac{24x}{6} \\ \frac{2y}{1} \times \frac{6}{6} = \frac{12y}{6} \\ \frac{24x}{6} + \frac{12y}{6} = \frac{31}{6} \\ 24x + 12y = 31$

$6x - y = \frac{43}{4} \\ \frac{6x}{1} \times \frac{4}{4} = \frac{24x}{4} \\ \frac{ - y}{1} \times \frac{4}{4} = \frac{ - 4y}{4} \\ \frac{24x}{4} - \frac{4y}{4} = \frac{43}{4 } \\ 24x - 4y = 43$

$24x + 12y = 31 \: ( \times - 1) \\ 24x - 4y = 43 \\ - 24x - 12y = - 31 \\ 24x - 4y = 43 \\ - 16y = 12 \\ 16y = - 12 \\ y = \frac{ - 12}{16} = \frac{ - 3}{4 } \\ y = \frac{ - 3}{4}$

$24x + 12y = 31 \\ 24x = 31 - 12y \\ x = \frac{31 - 12y}{24} = \frac{31 - 12 \times \frac{ - 3}{4} }{24} = \\ = \frac{ \frac{124}{4} - \frac{ - 36}{4} }{24} = \frac{ \frac{160}{4} }{24} = \frac{160}{4} \times \frac{1}{24} = \\ = \frac{ 160}{96} = \frac{5}{3 } \\ x = \frac{5}{3}$

$4 \times \frac{5}{3} + 2 \times \frac{ - 3}{4} = \frac{31}{6}$

$6 \times \frac{5}{3} - 4 \times \frac{ - 3}{4} = \frac{43}{4}$

espero te sirva