Question

5 autoturisme si 8 camioane consuma 81 l de benzina la 100 in parcursi ,iar 8 autoturisme si 4 camioane consuma 68 l de benzina la 100 km. Câți l de benzina consuma un autoturism la 100 km? Dar un camion?

Answer 1

$\left\{\begin{matrix} 5a + 8c = 81\\ 8a + 4c = 68 \: | \times ( - 2)\end{matrix}\right.$

$\left\{\begin{matrix} 5a + 8c = 81\\ - 16a - 8c = - 136\end{matrix}\right.$

$5a - 16a + 8c - 8c = 81 - 136$

$- 11a = - 55 \: | \div ( - 11)$

$a = 5$

$5a + 8c = 81$

$5 \times 5 + 8c = 81$

$25 + 8c = 81$

$8c = 81 - 25$

$8c = 56$

$c = \frac{56}{8}$

$c = 7$

Answer 2

5a..... 8c...... 81 l
8a..... 4c...... 68 l |×2
16a.... 8c....... 136
16a-5a =11a
136-81l =55l
11a........ 55l
a=55:11
a=5 l
5×5l..... 8×x l.... 81
25l..... 8xl....... 81
81-25=56
56:8=7 l