Question

Se 3a + 8b = 45 e 5a + 6b = 53.determine o valor de a-b

Answer 1

$\begin{cases}3a+8b=45\\ 5a+6b=53\end{cases}\\\\\\\\3a+8b=45\to~~ 3a=-8b+45\to~~a= \dfrac{-8b+45}{3} \\\\\\\\ 5a+6b=53\to~ 5\left( \dfrac{-8b+45}{3} \right)+6b=53\to~~ \dfrac{-40b+225}{3} +6b=53\to\\\\\\ mmc=3\to~ -40b+225+18b=159\to~~ -40b+18b=159-225\to\\\\\\ -22b=-66~(-1)\to~~ 22b=66\to~~b= \dfrac{66}{22} \to~~\large\boxed{b=3}$




$a= \dfrac{-8b+45}{3}\to~~ a= \dfrac{-8.3+45}{3}\to~~a= \dfrac{-24+45}{3}\to\\\\\\ a= \dfrac{21}{3}\to~~ \large\boxed{a=7}\\\\\\\\\\\\ \Large\boxed{\boxed{S=\{7~;~3\}}}$





$a-b\to~~7-3\to~~\Large\boxed{4}$