Toán Lớp 7: cho x- 2y + 3z = 56 biết x/6 = y/-7 ; x/3 = z/8

Question

Toán Lớp 7:  cho x- 2y + 3z = 56 biết x/6 = y/-7 ; x/3 = z/8

minhtuyethue · Answer

Giải đáp:   $  $   C&oacute; : x/6 = y/(-7) (1)   C&oacute; : x/3 = z/8   &harr; x/6 = z/16 (2)   Từ (1), (2)   -> x/6 = y/(-7) = z/16   &harr; x/6= (2y)/(-14) = (3z)/48   &Aacute;p dụng t&iacute;nh chất d&atilde;y tỉ số bằng nhau c&oacute; :   x/6 = (2y)/(-14) = (3z)/48 = (x - 2y+3z)/(6 - (-14) + 48) = 56/68 = 14/17   &harr;   ( left {  begin{array}{l} dfrac{x}{6}= dfrac{14}{17}    dfrac{2y}{-14}= dfrac{14}{17}    dfrac{3z}{48}= dfrac{14}{17} end{array}  right. )     &harr;  ( left {  begin{array}{l}x=6&times; dfrac{14}{17}   2y = -14 &times;  dfrac{14}{17}  3z=48&times; dfrac{14}{17} end{array}  right. )     &harr;  ( left {  begin{array}{l}x= dfrac{84}{17}  2y= dfrac{-196}{17}  3z= dfrac{672}{17} end{array}  right. )     &harr;  ( left {  begin{array}{l}x= dfrac{84}{17}  y= dfrac{-196}{17}&divide;2  z= dfrac{672}{17}&divide;3 end{array}  right. )     &harr;  ( left {  begin{array}{l}x= dfrac{84}{17}  y= dfrac{-98}{17}  z= dfrac{224}{17} end{array}  right. )     Vậy (x;y;z) = (84/17; (-98)/17; 224/17)

quynhmaithu · Answer

Ta c&oacute; :   x/3 = z/8   -> x/6 = z/16   -> x/6 =  y/{-7} = z/16   -> x/6 = {2y}/{-14} = 3z/{48}   Theo t&iacute;nh chất d&atilde;y tỉ số bằng nhau :   -> x/6 = {2y}/{-14} = 3z/{48} = {x-2y+3z}/{6 - (-14) + 48} = 14/17   -> x = 14/17 . 6 =  84/17    -> 2y = -196/17 -> y = -98/17   -> 3z = 672/17 -> z = 224/17   Vậy x = 84/17 v&agrave; y = -98/17 v&agrave; z = 224/17