Toán Lớp 7: 3(x-1)=2(y-2);4(y-2)=3(z-3) và 2x+3y-z=50

Question

Toán Lớp 7:  3(x-1)=2(y-2);4(y-2)=3(z-3) và 2x+3y-z=50

phuongthaongoc · Answer

3( x - 1 ) = 2( y - 2 ) 6( x - 1 ) = 4( y - 2 ) m&agrave; 4( y - 2 ) = 3( z - 3 ) $ Rightarrow$ 6( x - 1 ) = 4( y - 2 ) = 3( z - 3 ) $ Rightarrow$ $ dfrac{6( x - 1 )}{12}$ = $ dfrac{4( y - 2 )}{12}$ = $ dfrac{3( z - 3 )}{12}$ $ Rightarrow$ $ dfrac{x - 1}{2}$ = $ dfrac{y - 2}{3}$ = $ dfrac{z - 3}{4}$                           &Aacute;p dụng t/c DTSBN, ta c&oacute; :  $ dfrac{x - 1}{2}$ = $ dfrac{y - 2}{3}$ = $ dfrac{z - 3}{4}$ = $ dfrac{2x - 2}{4}$ = $ dfrac{3y - 6}{9}$ =  $ dfrac{2x - 2 + 3y - 6 - z}{9}$ = $ dfrac{( 2x + 3y - z ) - ( 2 + 6 )}{9}$ = $ dfrac{14}{3}$ $ Rightarrow$ $ begin{cases} x =  dfrac{31}{3}  y = 16  z =  dfrac{68}{3} end{cases}$                        Vậy x = $ dfrac{31}{3}$ ; y = 16 ; z = $ dfrac{68}{3}$

danvanthu · Answer

$ text{ 3( x - 1 ) = 2( y - 2 ) }$   $ Rightarrow$ $ text{ 6( x - 1 ) = 4( y - 2 ) }$   $ text{ m&agrave; 4( y - 2 ) = 3( z - 3 ) }$   $ Rightarrow$ $ text{ 6( x - 1 ) = 4( y - 2 ) = 3( z - 3 ) }$   $ Rightarrow$ $ text{ $ dfrac{6( x - 1 )}{12}$ = $ dfrac{4( y - 2 )}{12}$ = $ dfrac{3( z - 3 )}{12}$ }$   $ Rightarrow$ $ text{ $ dfrac{x - 1}{2}$ = $ dfrac{y - 2}{3}$ = $ dfrac{z - 3}{4}$ }$                           $ text{ &Aacute;p dụng t&iacute;nh chất d&atilde;y tỉ số bằng nhau, ta c&oacute; : }$    $ dfrac{x - 1}{2}$ = $ dfrac{y - 2}{3}$ = $ dfrac{z - 3}{4}$ = $ dfrac{2x - 2}{4}$ = $ dfrac{3y - 6}{9}$ = $ dfrac{( 2x - 2 ) + ( 3y - 6 ) - z }{4 + 9 - 4}$ = $ dfrac{2x - 2 + 3y - 6 - z}{9}$ = $ dfrac{( 2x + 3y - z ) - ( 2 + 6 )}{9}$ = $ dfrac{50 - 8}{9}$ = $ dfrac{14}{3}$   $ Rightarrow$ $ begin{cases} x -1 =  dfrac{14}{3}. 2 =  dfrac{28}{3}  y - 2 =  dfrac{14}{3}. 3 = 14  z - 3 =  dfrac{14}{3}. 4 =  dfrac{56}{3} end{cases}$    $ Rightarrow$ $ begin{cases} x =  dfrac{31}{3}  y = 16  z =  dfrac{68}{3} end{cases}$                         $Vậy$ ( $x$ ; $y$ ; $z$ ) $=$ ( $ dfrac{31}{3}$ ; $16$ ; $ dfrac{68}{3}$ }