Question

a/56 = b/7 y a-b=7
Porfis
Ayuda

Answer 1

Respuesta:

$a = \frac{51}{7} \: \: \: \: \: \: \: b = \frac{2}{7}$

Explicación paso a paso:

$\frac{a}{56} = \frac{b}{7} \\ a・7 = 56・b \\ 7a = 56b \\ 7a - 56b = 0 \\ \\ {\displaystyle\left\{{\begin{matrix}7a - 56b = 0 \\ a - b = 7\end{matrix}}\right.}</p><p></p><p>$

Resolvemos el sistema de ecuaciones

${\displaystyle\left\{{\begin{matrix}7a - 56b = 0 & (1)\\ a - b = 7& (2)\end{matrix}}\right.}$

Despejamos a de (2)

$a = 7 + b \: \: \: \: (3)$

Sustituimos (3) en (1)

$7a - 56b = 0 \\ 7(7 +b) - 56b = 0 \\ 14 + 7b - 56b = 0 \\ 7b - 56b = - 14 \\ - 49b = - 14 \\ b = \frac{ - 14}{ - 49} \\\fbox{b = \frac{2}{7} }$

Sustituimos 'b' en (3)

$a = 7 + b \\ a = 7 + \frac{2}{7} \\ a = \frac{49 + 2}{7} \\ \fbox{a = \frac{51}{7}}$

Comprobamos

$a - b = 7 \\ \frac{51}{7} - \frac{2}{7} = 7 \\ \frac{357 - 14}{49} = 7 \\ \frac{343}{49} = 7 \\ 7 = 7$