Question

Tìm các số nguyên \(x\) và \(y\), biết :

                \(\dfrac{x-3}{y-2}=\dfrac{3}{2}\) và \(x-y=4\)

Answer 1

Giải :

\(\dfrac{x-3}{y-2}=\dfrac{3}{2}\) nên 2(x-3) = 3(y-2)

Do đó : 2x - 6 = 3y - 6 nên 2x = 3y

\(\Rightarrow\) 2x - 2y = y hay 2(x-y) = y

Nên 2.4 = y

Vậy : \(y=8;x=\dfrac{3y}{2}=\dfrac{3.8}{2}=12\)

Answer 2

\(\dfrac{x-3}{y-2}=\dfrac{3}{2}\)

\(\Rightarrow\left(x-3\right)\cdot2=3\cdot\left(y-2\right)\)

\(\Rightarrow2x-6=3y-6\)

\(\Rightarrow2x=3y\)

\(\Rightarrow\dfrac{x}{y}=\dfrac{3}{2}\)

mà x - y = 4

\(\Rightarrow\left\{{}\begin{matrix}x=4:\left(3-2\right)\cdot3=12\\y=4:\left(3-2\right)\cdot2=8\end{matrix}\right.\)

Answer 3

nên 2(x – 3) = 3(y – 2)

Do đó 2x – 6 = 3y – 6 nên 2x = 3y

Suy ra 2x – 2y = y hay 2(x – y) = y

Nên 2.4 = y

Vậy y = 8, x = 3y / 2 = 3.8 /2 = 12

Answer 4

nên 2(x – 3) = 3(y – 2)

Do đó 2x – 6 = 3y – 6 nên 2x = 3y

Suy ra 2x – 2y = y hay 2(x – y) = y

Nên 2.4 = y

Vậy y = 8, x = 3y / 2 = 3.8 / 2 = 12