Question

Tìm các số nguyên x và y, biết

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

 

Answer 1

Ta có: \(\frac{x-3}{y-2}=\frac{3}{2}\)

=> (x - 3) . 2 = (y - 2) . 3

=> 2x - 6 = 3y - 6

=> 2x = 3y

=> x = 3/2y

Khi đó, ta có: x - y = 4

hay 3/2y - y = 4

=> 1/2y = 4

=> y = 4 : 1/2

=> y = 8

=> x = 4 + 8 = 12

Vậy x = 12 và y = 8

Answer 2

Theo đề:\(\frac{x-3}{y-2}=\frac{3}{2}\Rightarrow2\left(x-3\right)=3\left(y-2\right)\)

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

\(\Rightarrow2y-3y=-6+6\)

Vì\(x-y=4\Rightarrow x=4+y\)

\(\Rightarrow2\left(y+4\right)-3y=0\)

\(\Rightarrow2y+8-3y=0\)

\(\Rightarrow-y=-8\Rightarrow y=8\)

\(\Rightarrow x=y+4=8+4=12\)

Vậy y=8;x=12

Answer 3

\(x-y=4\Rightarrow x=4+y\)

\(\frac{x-3}{y-2}=\frac{3}{2}\Rightarrow\frac{4+y-3}{y-2}=\frac{3}{2}\)

\(\Rightarrow\frac{y+1}{y-2}=\frac{3}{2}\)

\(\Rightarrow\left(y+1\right)\cdot2=\left(y-2\right)\cdot3\)

\(\Rightarrow2y+2=3y-6\)

\(\Rightarrow3y-2y=6+2\)

\(\Rightarrow y=8\)

Thay y vào x - y = 4. Ta có:

\(x-y=4\Rightarrow x-8=4\)

\(\Rightarrow x=8+4=12\)

Answer 4

x = 6

y =2