Question

sistema de ecuaciones lineales utilizando el método de igualación​

Answer 1

Respuesta:

x=22/21. y=2/21

Explicación paso a paso:

$de \: la \: primera \: ecuacion \\ \\ 3x + 9y = 4 \\ 3x = 4 - 9y \\ x = \frac{4 - 9y}{3} \\ de \: la \: segunda \\ 2x - y = 2 \\ 2x = 2 + y \\ x = \frac{2 + y}{2}$

igualamos

$\frac{4 - 9y}{3} = \frac{2 + y}{2} \\ 8 - 18y = 6 + 3y \\ - 6 + 8 = 3y + 18y \\ 2 = 21y \\ y = \frac{2}{21}$

buscamos x

$x = \frac{2 + y}{2} = \frac{2 + \frac{2}{21} }{2} = \frac{ \frac{42}{21} + \frac{2}{21} }{2} = \\ \frac{ \frac{ \frac{44}{21} }{2} }{1} = \frac{44}{21} \times \frac{1}{2} = \frac{44}{22} = \frac{22}{21} \\ x = \frac{22}{21}$

comprobamos

$3 \times \frac{22}{21} + 9 \times \frac{2}{21} = \frac{66}{21} + \frac{18}{21} = \frac{84}{21} = 4$

$2 \times \frac{22}{21} - \frac{2}{21} = \frac{44}{21} - \frac{2}{21} = \frac{42}{21} = 2$

espero te sirva