Question

\(\dfrac{5z-6y}{4}\)=\(\dfrac{6x-4z}{5}\)=\(\dfrac{4y-5x}{6}\)và 3x-2y+5z= 96

Answer 1

từ \(\dfrac{5z-6y}{4}\)=\(\dfrac{6x-4z}{5}\)=\(\dfrac{4y-5x}{6}\)

=>\(\dfrac{20z-24y}{10}\)=\(\dfrac{30x-20z}{25}\)=\(\dfrac{24y-30x}{36}\)

=>\(\dfrac{20z-24y+30x-20z+24y-30x}{10+25+36}\)=0

=>20z - 24y = 30x - 20z = 30x - 20z = 24y - 30x = 0

=>20z = 24y = 15x => \(\dfrac{x}{4}\)=\(\dfrac{y}{5}\)=\(\dfrac{z}{6}\) => \(\dfrac{3x}{12}\)=\(\dfrac{2y}{10}\)=\(\dfrac{5z}{30}\)

=\(\dfrac{3x-2y+5z}{12-10+30}\) = 3

\(\dfrac{3x}{12}\)= 3 => 3x= 36 => x= 12

\(\dfrac{2y}{10}\)=3 => 2y= 30 => y=15

\(\dfrac{5z}{30}\)=3 => 5z= 90 => z= 18

vậy x=12, y=15, z=18