x=5

y=\(\frac{1}{4}\)

x=5

Ta có: 1+2y/18=1+4y/24  

=>  24(1+2y)=18(1+4y)   

  =>24+48y=18+72y 

   =>24-18=72y-48y   

  =>6=24y   

=>  y=1/4

    thay y=1/4 vào đề ta có: 

(1+ 1/2)/18=1+1/24=(1+3/2)/6x  

  =>1/12=(5/2)/6x  

  => 12(5/2)=6x 

   =>30=6x  

=>x=5                                  

Vậy x=5 

   y=1/4

\(\frac{1+4y}{18}=\frac{1+5y}{24}\Rightarrow24+96y=18+90y\)

\(\Rightarrow6+6y=0\Leftrightarrow6\left(1+y\right)=0\)Vậy y = -1

Thay y = -1 ta có :

\(\frac{1-5}{24}=\frac{1-6}{6x}\Leftrightarrow\frac{-5}{30}=-\frac{5}{6x}\left(\frac{-4}{24}=-\frac{5}{30}=\frac{1-5}{24}\right)\)

Vậy 6x = 30 hay x = 5 

Ta có: 1 + 2y/18 = 2.(1+2y)/2.18 = 2+4y/36

Sử dụng tc dãy tỉ số bằng nhau ta có:

2+4y/36 = 1+4y/24 = 2+4y-1-4y/36-24 = 1/12

Do 1+2y/18 = 1/12=> y = 1/4

1+6y/6x = 1/12=> x = 5

Vậy x = 5; y = 1/4

Áp dụng tính chất dãy tỉ số bằng nhau:

​​\(\frac{1+2y}{18}=\frac{1+4y}{24}=\frac{1+6y}{6x}=\frac{1+2y+1+6y}{18+6x}=\frac{8y+2}{18+6x}\)

suy ra

\(\frac{1+4y}{24}=\frac{8y+2}{18+6x}=\frac{2\left(1+4y\right)}{2\left(9+3x\right)}=\frac{1+4y}{9+3x}\)

=>9+3x=24

        3x=24-9

        3x=15

          x=15:3

          x=5

TK CHO MÌNH NHA

6y6yt6

Áp dụng dãy tỉ số bằng nhau, ta có:

\(\frac{1+2y}{18}=\frac{1+6y}{6x}=\frac{1+2y+1+6y}{18+6x}=\frac{2+8y}{18+6x}=\frac{2.1+4y}{2.9+3x}=\frac{1+4y}{9+3x}\)

\(\Rightarrow\frac{1+4y}{9+3x}=\frac{1+4y}{24}\Rightarrow9+3x=24\)

\(3x=15\)

Vậy: \(x=5\)

Ta có:

\(\frac{1+2y}{18}=\frac{1+4y}{24}\)

\(\Rightarrow\left(1+2y\right).24=\left(1+4y\right).18\)

\(\Rightarrow24+48y=18+72y\)

\(\Rightarrow24-18=72y-48y\)

\(\Rightarrow24y=6\)

\(\Rightarrow y=6:24=\frac{1}{4}\)

Thay \(y=\frac{1}{4}\) vào đề bài ta có:

\(\frac{1+2.\frac{1}{4}}{18}=\frac{1+6.\frac{1}{4}}{6x}\)

\(\Rightarrow\frac{1+\frac{1}{2}}{18}=\frac{1+\frac{3}{2}}{6x}\)

\(\Rightarrow\frac{\frac{3}{2}}{18}=\frac{\frac{5}{2}}{6x}\)

=> \(\frac{3}{2}.6x=\frac{5}{2}.18\)

\(\Rightarrow9x=45\)

\(\Rightarrow x=45:9=5\)

Vậy \(x=5;y=\frac{1}{4}\)

ĐK: x#0
Ta có:
(1) 1+2y/18 = 1+4y/24
=> 24 + 48y = 18 + 72y
<=> y=1/4
(2) 1+4y/24=1+6y/6x
Thay y=1/4 vào (2) ta tìm đc x=5 (TMĐK)

Theo đề bài, ta có;

\(\frac{1+2y}{18}=\frac{1+4y}{24}\)

\(\Rightarrow24\times\left(1+2y\right)=18\times\left(1+4y\right)\)

\(\Rightarrow24+48y=18+72y\)

\(\Rightarrow48y-72y=18-24\)

\(\Rightarrow-24y=-6\)

\(\Rightarrow y=\frac{-6}{-24}\)

\(\Rightarrow y=\frac{1}{4}\)

Với \(y=\frac{1}{4}\), ta có:

\(\frac{1+4y}{24}=\frac{1+6y}{6x}\) \(\left(x\ne0\right)\)

\(\Rightarrow\frac{1+4\times\frac{1}{4}}{24}=\frac{1+6\times\frac{1}{4}}{6x}\)

\(\Rightarrow\frac{1+1}{24}=\frac{1+\frac{3}{2}}{6x}\)

\(\Rightarrow\frac{2}{24}=\frac{\frac{5}{2}}{6x}\)

\(\Rightarrow\frac{1}{12}=\frac{\frac{5}{2}}{6x}\)

\(\Rightarrow6x=\frac{5}{2}\div\frac{1}{12}\)

\(\Rightarrow6x=\frac{5}{2}\times12\)

\(\Rightarrow6x=30\)

\(\Rightarrow x=30\div6\)

\(\Rightarrow x=5\)

Vậy \(x=5\) và \(y=\frac{1}{4}\) thì thỏa mãn đề bài.

Áp dụng tính chất dãy số bằng nhau ta có:

\(\frac{1+2y}{18}=\frac{1+4y}{24}=\frac{1+6y}{6x}=\frac{2y+8y}{18+6x}=\frac{2.\left(1+4y\right)}{2.\left(9+3x\right)}=\frac{1+4y}{9+3x}\)

\(\Rightarrow\frac{1+4y}{9+3x}=\frac{1+4y}{24}\Rightarrow9+3x=24\)

\(3x=15\)

\(x=15\)