a)
Theo đề ta có:
\(\dfrac{3x}{5}=\dfrac{2y}{4}\) và \(6x+4y=15\)
Áp dung tính chất của dãy tỉ số bằng nhau ta có:
\(\dfrac{3x}{5}=\dfrac{2y}{4}=\dfrac{6x}{10}=\dfrac{4y}{8}=\dfrac{6x+4y}{10+8}=\dfrac{15}{18}=\dfrac{5}{6}\)
\(\dfrac{3x}{5}=\dfrac{5}{6}\Rightarrow3x=\dfrac{5}{6}.5=\dfrac{25}{6}\Rightarrow x=\dfrac{25}{6}:3=\dfrac{25}{18}\)
\(\dfrac{2y}{4}=\dfrac{5}{6}\Rightarrow2y=\dfrac{5}{6}.4=\dfrac{10}{3}\Rightarrow y=\dfrac{10}{3}:2=\dfrac{5}{3}\)
Vậy \(x=\dfrac{25}{18}\) ; \(y=\dfrac{5}{3}\)
b)
Theo đề ta có:
\(\dfrac{3x}{5}=\dfrac{4y}{3}=\dfrac{5z}{7}\) và \(9x+8y+5z=10\)
Áp dung tính chất của dãy tỉ số bằng nhau ta có:
\(\dfrac{3x}{5}=\dfrac{4y}{3}=\dfrac{5z}{7}=\dfrac{9x}{15}=\dfrac{8y}{6}=\dfrac{9x+8y+5z}{15+6+7}=\dfrac{10}{28}=\dfrac{5}{14}\)
\(\dfrac{3x}{5}=\dfrac{5}{14}\Rightarrow3x=\dfrac{5}{14}.5=\dfrac{25}{14}\Rightarrow x=\dfrac{25}{14}:3=\dfrac{25}{42}\)
\(\dfrac{4y}{3}=\dfrac{5}{14}\Rightarrow4y=\dfrac{5}{14}.3=\dfrac{15}{14}\Rightarrow y=\dfrac{15}{14}:4=\dfrac{15}{56}\)
\(\dfrac{5z}{7}=\dfrac{5}{14}\Rightarrow5z=\dfrac{5}{14}.7=\dfrac{5}{2}\Rightarrow z=\dfrac{5}{2}:5=\dfrac{1}{2}\)
Vậy \(x=\dfrac{25}{42}\) ; \(y=\dfrac{15}{56}\) ; \(z=\dfrac{1}{2}\)
Ai có lòng giúp tớ với ạ
Tớ đang cần gấp ạ
Từ \(\dfrac{x}{2y}\)=\(\dfrac{3}{5}\) =>\(\dfrac{x}{3}\)=\(\dfrac{2y}{5}\)
Đặt \(\dfrac{x}{3}\)=\(\dfrac{2y}{5}\)=k =>x=3k,y=\(\dfrac{5k}{2}\)
Theo đề bài,ta có:
4x - 5y = -64
=>4.3k - 5.\(\dfrac{5k}{2}\) = -64
12k -\(\dfrac{25k}{2}\)= -64
\(\dfrac{24k}{2}\)-\(\dfrac{25k}{2}\)= -64
\(\dfrac{-k}{2}\)= -64
=> -k= -64.2= -128
=>k=128
Thay k=128,ta có:
\(\dfrac{x}{3}\)=128 =>x=128.3=384
\(\dfrac{2y}{5}\)=128 =>y=\(\dfrac{128.5}{2}\)=320
Vậy x=384,y=320
