a, y \(\times\) \(\dfrac{4}{3}\) = \(\dfrac{16}{9}\)

    y         =    \(\dfrac{16}{9}\) : \(\dfrac{4}{3}\)

    y         = \(\dfrac{4}{3}\)

b, ( y - \(\dfrac{1}{2}\)) + 0,5 = \(\dfrac{3}{4}\)

    y - 0,5 + 0,5 = \(\dfrac{3}{4}\)

   y                   = \(\dfrac{3}{4}\)

c, \(\dfrac{4}{5}-\dfrac{2}{5}y\) = 0,2

   0,8 - 0,4y = 0,2

           0,4y = 0,8 - 0,2

           0,4y  = 0,6

               y = 1,5

d, (y + \(\dfrac{3}{4}\)) \(\times\) \(\dfrac{5}{7}\) = \(\dfrac{10}{9}\)

    y + \(\dfrac{3}{4}\)           = \(\dfrac{10}{9}\) : \(\dfrac{5}{7}\)

   y + \(\dfrac{3}{4}\)            = \(\dfrac{14}{9}\)

y                    = \(\dfrac{14}{9}\) - \(\dfrac{3}{4}\)

 y                   =   \(\dfrac{29}{36}\)

e, y : \(\dfrac{5}{4}\)         = \(\dfrac{9}{5}\)  + \(\dfrac{1}{2}\)

   y : \(\dfrac{5}{4}\)         =   \(\dfrac{23}{10}\)

  y                =      \(\dfrac{23}{10}\)

  y               =   \(\dfrac{23}{8}\)

f, y \(\times\) \(\dfrac{1}{2}\) + \(\dfrac{3}{2}\) \(\times\) y   = \(\dfrac{4}{5}\)

   y \(\times\) ( \(\dfrac{1}{2}+\dfrac{3}{2}\))      =  \(\dfrac{4}{5}\)

   2y                       = \(\dfrac{4}{5}\)

    y                        = \(\dfrac{2}{5}\)

1)\(\left(x+1\right).\left(y-2\right)=0\)                                       \(\left(x,y\inℤ\right)\)

\(\Rightarrow\orbr{\begin{cases}x+1=0\\y-2=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1\\y=2\end{cases}}\)

2)\(\left(x-5\right).\left(y-7\right)=1\)

3)\(\left(x+4\right).\left(y-2\right)=2\)

4)\(\left(x-4\right).\left(y+3\right)=-3\)

5)\(\left(x+3\right).\left(y-6\right)=-4\)

6)\(\left(x-8\right).\left(y+7\right)=5\)

7)\(\left(x+7\right).\left(y-3\right)=-6\)

8)\(\left(x-6\right).\left(y+2\right)=7\)

ok :)

Bài 2:

\(\dfrac{a+b}{a-b}=\dfrac{c+a}{c-a}\)

\(\Rightarrow\dfrac{a+b}{c+a}=\dfrac{a-b}{c-a}=\dfrac{a+b+a-b}{c+a+c-a}=\dfrac{a}{c}\) (T/c dãy tỷ số = nhau)

\(\Rightarrow\dfrac{a+b}{c+a}=\dfrac{a}{c}\Rightarrow c\left(a+b\right)=a\left(c+a\right)\)

\(\Rightarrow ac+bc=ac+a^2\Rightarrow a^2=bc\)

a) x=949/27
    y=755/27
    z=61/9
    các bạn xem giúp mik đúng chx ạ, mik đặt là k

\(\frac{x}{y}=\frac{3}{4}\)và 2x + 5y = 10

=> \(\frac{x}{3}=\frac{y}{4}\)=> \(\frac{2x}{6}=\frac{5y}{20}\)

Áp dụng tính chất của dãy tỉ số bằng nhau ta có :

\(\frac{2x}{6}=\frac{5y}{20}=\frac{2x+5y}{6+20}=\frac{10}{26}=\frac{5}{13}\)

=> 2x = \(\frac{30}{13}\)=> x = \(\frac{15}{13}\)

     5y = \(\frac{100}{13}\)=> y = \(\frac{20}{13}\)

Vậy x = \(\frac{15}{13}\); y = \(\frac{20}{13}\)

21x = 19y và x - y = 4

Ta có :

\(\frac{x}{19}=\frac{y}{21}\)và x - y = 4

Áp dụng tính chất của dayc tỉ số bằng nhau là :

\(\frac{x}{19}=\frac{y}{21}=\frac{x-y}{19-21}=\frac{4}{-2}=-2\)

=> x = -38

     y = -42

Vậy x = - 38 ; y = - 42

\(\frac{x}{5}=\frac{y}{3}\)và x ² - y ² = 4

Đặt \(\frac{x}{5}=\frac{y}{3}=k\)

=> x = 5k , y = 3k

=> x ² - y ² = ( 5 k ) ² - ( 3 k ) ² = 25k ² - 9 k ²  = 4

                                                  16 k ²        = 4

                                                       k ²        = \(\frac{1}{4}\)

                                            => k = \(\frac{1}{2}\)hoặc x = \(\frac{-1}{2}\)

+ Xét k = \(\frac{1}{2}\)ta có :

=> x = \(\frac{5}{2}\)và y = \(\frac{3}{2}\)

+Xét  k = \(\frac{-1}{2}\)

=> x = \(\frac{-5}{2}\), y = \(\frac{-3}{2}\)

Vậy x = \(\frac{5}{2}\)và y = \(\frac{3}{2}\)

hoặc x = \(\frac{-5}{2}\), y = \(\frac{-3}{2}\)

\(\dfrac{2}{5}\) x y : \(\dfrac{7}{4}\) = \(\dfrac{7}{8}\)

\(\dfrac{2}{5}\) x y = \(\dfrac{7}{8}\) x \(\dfrac{7}{4}\)

 \(\dfrac{2}{5}\) x y = \(\dfrac{49}{32}\)

         y = \(\dfrac{49}{32}\) : \(\dfrac{2}{5}\)

         y = \(\dfrac{245}{64}\)

2\(\dfrac{2}{5}\): y x 1\(\dfrac{1}{4}\) = 2\(\dfrac{3}{5}\)

\(\dfrac{12}{5}\): y x \(\dfrac{5}{4}\) = \(\dfrac{13}{5}\)

\(\dfrac{12}{5}\): y        = \(\dfrac{13}{5}\): \(\dfrac{5}{4}\)

 \(\dfrac{12}{5}\): y = \(\dfrac{52}{25}\)

        y = \(\dfrac{12}{5}\): \(\dfrac{52}{25}\)

        y = \(\dfrac{15}{13}\)

\(\dfrac{12}{5}\) - 1\(\dfrac{2}{5}\) \(\times\) y = 1\(\dfrac{1}{4}\)

 \(\dfrac{12}{5}\) - \(\dfrac{7}{5}\) \(\times\) y  = \(\dfrac{5}{4}\)

           \(\dfrac{7}{5}\) \(\times\) y  = \(\dfrac{12}{5}\) - \(\dfrac{5}{4}\)

            \(\dfrac{7}{5}\) \(\times\) y = \(\dfrac{23}{20}\)

                   y = \(\dfrac{23}{20}\) : \(\dfrac{7}{5}\)

                   y = \(\dfrac{23}{28}\)

1) 2^{2x + 1} = 32

=> 2^{2x + 1} = 2⁵

=> 2x + 1 = 5

=> 2x = 5 - 1

=> 2x = 4

=> x = 2

(2) 3.x³ - 100 = 275

=> 3x³ = 275 + 100

=> 3x³ = 375

=> x³ = 375 : 3

=> x³ = 125

=> x³ = 5³

=> x = 5

(4) (x - 1)³ - 2⁵ = 7²

=> (x - 1)³ = 49 + 32

=> (x - 1)³ = 81

(xem lại đề)

5) Áp dụng t/c của dãy tỉ số bằng nhau, ta có:

  \(\frac{x}{3}=\frac{y}{5}=\frac{x-y}{3-5}=\frac{-4}{-2}=2\)

=> \(\hept{\begin{cases}\frac{x}{3}=2\\\frac{y}{5}=2\end{cases}}\) => \(\hept{\begin{cases}x=2.3=6\\y=2.5=10\end{cases}}\)

Vậy ...

6) Ta có: \(\frac{x}{2}=\frac{y}{3}\) => \(\frac{x}{10}=\frac{y}{15}\)

       \(\frac{y}{5}=\frac{z}{4}\) => \(\frac{y}{15}=\frac{z}{12}\)

=> \(\frac{x}{10}=\frac{y}{15}=\frac{z}{12}\)

Áp dụng t/c của dãy tỉ số bằng nhau, ta có:

 \(\frac{x}{10}=\frac{y}{15}=\frac{z}{12}=\frac{x+y+z}{10+15+12}=\frac{-49}{37}\)

=> \(\hept{\begin{cases}\frac{x}{10}=-\frac{49}{37}\\\frac{y}{15}=-\frac{49}{37}\\\frac{z}{12}=-\frac{49}{37}\end{cases}}\) => \(\hept{\begin{cases}x=-\frac{49}{37}\cdot10=\frac{-490}{37}\\y=-\frac{49}{37}\cdot15=-\frac{735}{37}\\z=-\frac{49}{37}\cdot12=-\frac{588}{37}\end{cases}}\)

Vậy ...

mk lm bài mà mk cho là ''khó'' nhất thôi nha 

\(\frac{x}{2}=\frac{y}{3};\frac{y}{5}=\frac{z}{4}\)và \(x+y+z=-49\)

\(\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{10}=\frac{y}{15}\left(1\right)\)

\(\frac{y}{5}=\frac{z}{4}\Rightarrow\frac{y}{15}=\frac{z}{12}\left(2\right)\)

Từ (1) và (2) \(\Rightarrow\frac{x}{10}=\frac{y}{15}=\frac{z}{12}\)

ADTC dãy tỉ số bằng nhau ta có 

\(\frac{x}{10}=\frac{y}{15}=\frac{z}{12}=\frac{x+y+z}{10+15+12}=-\frac{49}{37}\)

\(\Rightarrow\hept{\begin{cases}\frac{x}{10}=-\frac{49}{37}\\\frac{y}{15}=-\frac{49}{37}\\\frac{z}{12}=-\frac{49}{37}\end{cases}\Rightarrow\hept{\begin{cases}x=-\frac{49}{37}.10=-\frac{490}{37}\\y=-\frac{49}{37}.15=-\frac{735}{37}\\z=-\frac{49}{37}.12=-\frac{588}{37}\end{cases}}}\)