Question

1) 4x + 5y = 1
2) 3x − 2y = 18 por reducción e igualación

Answer 1

Respuesta:

1R= -4/5

2R= d3/2

Explicación paso a paso:

Answer 2

Explicación paso a paso:

igualación

4

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

igualamos

$\frac{8 + 2y}{3} = \frac{1 - 5y}{4} \\ 32 + 8y = 3 - 15y \\ - 3 + 32 = - 15 - 8y \\ 29 = - 23y \\ 23y = - 29 \\ y = \frac{ - 29}{23}$

buscamos x

$x = \frac{1 - 5y}{4} = \frac{1 - 5 \times \frac{ - 29}{23} }{4} = \\ \frac{ \frac{23}{23} - \frac{ - 145}{23} }{4} = \\ \frac{ \frac{ \frac{168}{23} }{4} }{1} = \frac{168}{23} \times \frac{1}{4} = \\ \frac{168}{92} = \frac{42}{23} \\ x = \frac{42}{23}$

reducción

$4x + 5y = 1( \times - 3) \\ 3x - 2y = 8( \times 4) \\ \\ - 12x - 15y = - 3 \9\ 12x - 8y = 32 \\ - 23y = 29 \\ 23y = - 29 \\ y = \frac{ - 29}{23} \\ buscamos \: x \\ \\ 4x + 5y = 1$

$4x + 5 \times \frac{ - 29}{23} = 1 \\ 4x = 1 - \frac{ - 145}{23} \\ 4x = \frac{23}{23} - \frac{ - 145}{23} = \frac{168}{23 } \\ x = \frac{ \frac{ \frac{168}{23} }{4} }{1} = \frac{168}{23} \times \frac{1}{4} = \frac{168}{92} = \frac{42}{23}$

comprobamos

$4 \times \frac{42}{23} + 5 \times \frac{ - 29}{23} = \frac{168}{23} + \frac{ - 145}{23} = \frac{ 23}{23} = 1$

$3 \times \frac{42}{23} - 2 \times \frac{ - 29}{23} = \frac{126}{23} - \frac{ - 58}{23} = \frac{184}{23} = 8$

espero te sirva