Question

método por igualación 5x+2y=13
x+3y=1​

Answer 1

Respuesta:

$y = \frac{ - 8}{13} \\ \\ x = \frac{37}{13}$

Explicación paso a paso:

$5x + 2y = 13 \\x + 3y = 1$

Despejar x en ambas ecuaciones:

$5x + 2y = 13 \\ \\ 5x = 13 - 2y \\ \\ x = \frac{13 - 2y}{5}$

$x + 3y = 1 \\ \\ x = 1 - 3y$

Igualar las y:

$\frac{13 - 2y}{5} =1 - 3y \\ \\ 13 - 2y = 5(1 - 3y) \\ \\ 13 - 2y = 5 - 15y \\ \\ - 2y + 15y = 5 - 13 \\ \\ 13y = - 8 \\ \\ y = \frac{ - 8}{13}$

Reemplazar Y:

$x + 3y = 1 \\ \\ x + 3( \frac{ - 8}{13} ) = 1 \\ \\ x - \frac{24}{13} = 1 \\ \\ x = 1 + \frac{24}{13} \\ \\ x = \frac{13(1) + (1)(24)}{13} \\ \\ x = \frac{13 + 24}{13} \\ \\ x = \frac{37}{13}$

Verificar:

$x + 3y = 1 \\ \\ \frac{37}{13} + 3( \frac{ - 8}{13} ) = 1 \\ \\ \frac{37}{13} + ( \frac{ - 24}{13} ) = 1 \\ \\ \frac{37}{13} - \frac{24}{13} = 1 \\ \\ \frac{37 - 24}{13} = 1 \\ \\ \frac{13}{13} = 1 \\ \\ 1 = 1$

Saludos!!✌