Question

Tìm x,y biết:

a, \(\frac{x}{5}=\frac{y}{7}\)và x.y =140

b, 7x= 3y và x.y = 2100

Answer 1

\(\frac{x}{5}=\frac{y}{7}=k\Rightarrow\hept{\begin{cases}x=5k\\y=7k\end{cases}}\)

\(x\cdot y=140\)

\(\Rightarrow5k\cdot7k=140\)

\(\Rightarrow35k^2=140\)

\(\Rightarrow k^2=4\)

\(\Rightarrow k=\pm2\)

\(k=2\Rightarrow\hept{\begin{cases}x=2\cdot5=10\\y=2\cdot7=14\end{cases}}\)

\(k=-2\Rightarrow\hept{\begin{cases}x=-2\cdot5=-10\\y=-2\cdot7=-14\end{cases}}\)

\(7x=3y\)

\(\Rightarrow\frac{x}{3}=\frac{y}{7}=k\Rightarrow\hept{\begin{cases}x=3k\\y=7k\end{cases}}\)

\(\Rightarrow x\cdot y=3k\cdot7k=2100\)

\(\Rightarrow21k^2=2100\)

\(\Rightarrow k^2=100\)

\(\Rightarrow k=\pm10\)

\(k=10\Rightarrow\hept{\begin{cases}x=10\cdot3=30\\y=10\cdot7=70\end{cases}}\)

\(k=-10\Rightarrow\hept{\begin{cases}x=-10\cdot3=-30\\y=-10\cdot7=-70\end{cases}}\)

Answer 2

4x=3y và 3x-y=21

Answer 3

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Answer 4

Ta có:

\(\frac{x}{5}=\frac{y}{7}\Rightarrow7x=5y\)

\(\Rightarrow7x^2=5xy\Rightarrow5\cdot140=7x^2\Rightarrow x^2=5\cdot20=100\)

\(\Rightarrow x=10;x=-10\)

Nếu \(x=10\Rightarrow y=14\)

Nếu \(x=-10\Rightarrow y=-14\)

Vậy ( x;y ) thỏa mãn là ( 10;14 );( -10;-14 )

Answer 5

Ta có

\(7x=3y\Rightarrow7xy=3y^2\Rightarrow3y^2=7\cdot2100\)

\(\Rightarrow y^2=4900\Rightarrow y=70;y=-70\)

Nếu \(y=70\Rightarrow x=2\)

Nếu \(y=-70\Rightarrow x=-2\)

Vậy các cặp ( x,y ) thỏa mãn là ( 70,2 );( -70;-2 )