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

c)\(\dfrac{3}{8}\times\dfrac{5}{8}+y=\dfrac{5}{4}\) 

   \(\dfrac{15}{64}+y=\dfrac{5}{4}\) 

           \(y=\dfrac{5}{4}-\dfrac{15}{64}\) 

           \(y=\dfrac{65}{64}\)

d, \(\dfrac{3}{8}+\dfrac{5}{8}\times y=\dfrac{5}{4}\) 

          \(\dfrac{5}{8}\times y=\dfrac{5}{4}-\dfrac{3}{8}\) 

          \(\dfrac{5}{8}\times y=\dfrac{7}{8}\) 

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

                \(y=\dfrac{7}{5}\)

a) 3/4 x y = 9/10

y = 9/10 : 3/4

y = 6/5

b) 3/5 : y = 7/20

y = 3/5 : 7/20 

y = 12/7

e)\(\dfrac{1}{3}+\dfrac{2}{3}:x=\dfrac{5}{2}\) 

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

       \(\dfrac{2}{3}:x=\dfrac{13}{6}\) 

             \(x=\dfrac{2}{3}:\dfrac{13}{6}\) 

             \(x=\dfrac{4}{13}\)

\(\frac{2}{3}x\frac{4}{y}=\frac{4}{45}:\frac{1}{5}\)\(=\frac{4}{15}\)

\(\frac{4}{y}=\frac{4}{15}:\frac{2}{3}\)\(=\frac{2}{5}\)

y=4:\(\frac{2}{5}\)    y=10

\(\frac{3}{4}x\frac{y}{5}=\frac{15}{4}\)

\(\frac{y}{5}=\frac{15}{4}:\frac{3}{4}=5\)

y=5x5=25

1) \(x+y=10\) mà \(x=y\) nên: \(x=y=\dfrac{10}{2}=5\)

2) \(2x+3y=180\) mà \(x=y\)

Ta có: \(2y+3y=180\Rightarrow5y=180\Rightarrow y=180:5=36\)

Vậy \(x=y=36\)

3) \(x+y=180\) mà \(x=y\) nên: \(x=y=\dfrac{180}{2}=90\)

4) \(3x+5y=13\) mà \(y=2x\) ta có:

\(3x+5\cdot2x=13\Rightarrow13x=13\Rightarrow x=1\)

\(y=2x=2\cdot1=2\)

Các câu còn lại bạn làm tương tự

a) \(\dfrac{10^{12}+5^{11}.2^9-5^{13}.2^8}{4.5^5.10^6}\)

\(=\dfrac{2^{12}.5^{12}+5^{11}.2^9-5^{13}.2^8}{2^2.5^5.2^6.5^6}\)

\(=\dfrac{2^{12}.5^{12}+5^{11}.2^9-5^{13}.2^8}{2^8.5^{11}}\)

\(=\dfrac{\left(2^8.5^{11}\right)\left(2^4.5+2-5^2\right)}{2^8.5^{11}}\)

\(=2^4.5+2-5^2\)

\(=57\)

b) \(\dfrac{\left[5\left(x-y\right)^4-3\left(x-y\right)^3+4\left(x-y\right)^2\right]}{\left(y-x\right)^2}\)

\(=\dfrac{\left(x-y\right)^2\left[5\left(x-y\right)^2-3\left(x-y\right)+4\right]}{\left(y-x\right)^2}\)

\(=\dfrac{\left(x^2+y^2-2xy\right)\left[5\left(x-y\right)^2-3\left(x-y\right)+4\right]}{\left(y^2+x^2-2xy\right)}\)

\(=5\left(x-y\right)^2-3\left(x-y\right)+4\)

c) \(\dfrac{\left(x+y\right)^5-2\left(x+y\right)^4+3\left(x+y\right)^3}{-5\left(x+y\right)^3}\)

\(=\dfrac{\left(x+y\right)^3\left[5\left(x+y\right)^2-2\left(x+y\right)+3\right]}{-5\left(x+y\right)^3}\)

\(=\dfrac{5\left(x+y\right)^2-2\left(x+y\right)+3}{-5}\)

2: y \(\times\) \(\dfrac{3}{5}\) = \(\dfrac{9}{10}\)

2:y =  \(\dfrac{9}{10}\) : \(\dfrac{3}{5}\) 

2: y = \(\dfrac{3}{2}\)

    y = 2 : \(\dfrac{3}{2}\)

     y = \(\dfrac{4}{3}\)

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

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

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

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

            y = \(\dfrac{8}{5}\)

\(\dfrac{3}{4}\) \(\times\) ( \(\dfrac{7}{2}\) - y) = \(\dfrac{3}{2}\)

           \(\dfrac{7}{2}\) - y = \(\dfrac{3}{2}\) : \(\dfrac{3}{4}\)

            \(\dfrac{7}{2}\) - y = 2

                   y = \(\dfrac{7}{2}\) - 2

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