2a = 3b; $\dfrac{a}{10}$ = $\dfrac{c}{5}$ và a + b - 2c = -30
Ta có:
2a = 3b ⇔ $\dfrac{a}{3}$ = $\dfrac{b}{2}$ ⇒ $\dfrac{a}{30}$ = $\dfrac{b}{20}$
$\dfrac{a}{10}$ = $\dfrac{c}{5}$ ⇒ $\dfrac{a}{30}$ = $\dfrac{c}{15}$
⇒ $\dfrac{a}{30}$ = $\dfrac{b}{20}$ = $\dfrac{c}{15}$
⇔ $\dfrac{a}{30}$ = $\dfrac{b}{20}$ = $\dfrac{2c}{30}$
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
$\dfrac{a}{30}$ = $\dfrac{b}{20}$ = $\dfrac{2c}{30}$ = $\dfrac{a + b - 2c }{30 + 20 - 30}$ = $\dfrac{-30}{20}$ = $\dfrac{-3}{2}$
Do đó:
$\dfrac{a}{30}$ = $\dfrac{-3}{2}$ ⇒ a = -45
$\dfrac{b}{20}$ = $\dfrac{-3}{2}$ ⇒ b = -30
$\dfrac{2c}{30}$ = $\dfrac{-3}{2}$ ⇔ $\dfrac{c}{15}$ = $\dfrac{-3}{2}$ = -20
