Áp dụng tính chất dãy các tỉ số bằng nhau, ta có:
`(3x - 2y)/37 = (5y - 3z)/15 = (2z - 5x)/2`
`= (5(3x - 2y))/(5. 37) = (2(5y - 3z))/(2. 15) = (3(2z - 5x))/(3. 2)`
`= (15x - 10y)/185 = (10y - 6z)/30 = (6z - 15x)/6`
`= (15x - 10y + 10y - 6z + 6z - 15x)/(185 + 30 + 6)`
`= 0/221`
`= 0`
`<=> (3x - 2y)/37 = (5y - 3z)/15 = (2z - 5x)/2 = 0`
`<=> 3x - 2y = 5y - 3z = 2z - 5x = 0`
`<=>` \(\left\{\begin{matrix}3x - 2y = 0\\5y - 3z = 0\\2z - 5x = 0\end{matrix}\right.\)
`<=>` \(\left\{\begin{matrix}3x = 2y\\5y = 3z\\2z = 5x\end{matrix}\right.\)
`<=>` \(\left\{\begin{matrix}\dfrac{x}{2} = \dfrac{y}{3}\\\dfrac{y}{3} = \dfrac{z}{5} \\\dfrac{z}{5} = \dfrac{x}{2}\end{matrix}\right.\)
`<=> x/2 = y/3 = z/5`
`<=>` \(\left\{\begin{matrix}\dfrac{x}{2} = \dfrac{y}{3}\\\dfrac{x}{2} = \dfrac{z}{5}\\\end{matrix}\right.\)
`<=>` \(\left\{\begin{matrix}y = \dfrac{3}{2}x\\z = \dfrac{5}{2}x\end{matrix}\right.\)
Thay \(\left\{\begin{matrix}y = \dfrac{3}{2}x\\z = \dfrac{5}{2}x\end{matrix}\right.\) vào `10x - 3y - 2z = -4`, ta được:
`10x - 3. 3/2x - 2. 5/2x = -4`
`<=> 10x - 9/2x - 5x = -4`
`<=> 1/2x = -4`
`<=> x = -8`
Với `x = -8 <=>` \(\left\{\begin{matrix}y = \dfrac{3}{2}. -8 = -12\\z = \dfrac{5}{2}. -8 = -20\end{matrix}\right.\)
Vậy \(\left\{\begin{matrix}x = -8\\y = -12\\z = -20\end{matrix}\right.\)
