Question

2x-3y=1
5x+2y=4
Ayudenme a resolverla por favor ​

Answer 1

Explicación paso a paso:

$2x - 3y = 1 \\ 2x = 1 + 3y \\ x = \frac{1 + 3y}{2} \\ 5x + 2y = 4 \\ 5x = 4 - 2y \\ x = \frac{4 - 2y}{5}$

igualamos

$\frac{1 + 3y}{2} = \frac{4 - 2y}{5} \\ 5 + 15y = 8 - 4y \\ - 8 + 5 = - 4y - 15y \\ - 3 = - 19y \\ 19y = 3 \\ y = \frac{3}{19}$

buscamos x

$x = \frac{1 + 3y}{2} = \frac{1 + 3 \times \frac{3}{19} }{2} = \frac{1 + \frac{9}{19} }{2} = \frac{ \frac{19}{19} + \frac{9}{19} }{2} = \frac{28}{19 } \times \frac{1}{2} = \frac{28}{34} = \frac{14}{19}$

$x = \frac{14}{19}$

$2 \times \frac{14}{19} - 3 \times \frac{3}{19} = \frac{28}{19} - \frac{9}{19} = \frac{19}{19} = 1$

$5 \times \frac{14}{19} + 2 \times \frac{3}{19} = \frac{70}{19} + \frac{6}{19} = \frac{76}{19} = 4$