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

Question

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

lyly98 · Answer

Giải đáp:   $  $   Đặt (x-1)/2 = (y-2)/3 = (z-3)/4 = k   &harr;   ( left {  begin{array}{l} dfrac{x-1}{2}=k    dfrac{y-2}{3}=k    dfrac{z-3}{4}=k end{array}  right. )     &harr;  ( left {  begin{array}{l}x-1=2k  y-2=3k  z-3=4k end{array}  right. )     &harr;  ( left {  begin{array}{l}x=2k+1   y=3k+2  z=4k+3 end{array}  right. ) (1)     C&oacute; : 2x + 3y - z=50     Thay (1) v&agrave;o ta được :     &harr;2 (2k + 1) + 3 (3k + 2) - (4k+3)=50     &harr;4k + 2 + 9k + 6 - 4k - 3 = 50     &harr; (4k + 9k - 4k) + (2 + 6 - 3) = 50     &harr; 9k+5=50     &harr;9k=50-5     &harr;9k=45     &harr;k=45&divide;9     &harr;k=5     Với k=5 thay v&agrave;o (1) ta được :     &harr;  ( left {  begin{array}{l}x=2&times;5+1  y=3&times;5+2  z=4&times;5+3 end{array}  right. )     &harr;  ( left {  begin{array}{l}x=10+1  y=15+2  z=20+3 end{array}  right. )     &harr;  ( left {  begin{array}{l}x=11  y=17  z=23 end{array}  right. )      Vậy (x;y;z) = (11;17;23)

ankim · Answer

C&oacute;: $ frac{x-1}{2}$ = $ frac{y-2}{3}$ =$ frac{z-3}{4}$ &rArr; $ frac{2x-2}{4}$ = $ frac{3y-6}{9}$ =$ frac{z-3}{4}$ = $ frac{2x-2+ 3y-6 -z+3}{4+9-4}$ = $ frac{50 -5}{9}$ = 5   &rArr;  $ frac{2x-2}{4}$ =5 &rArr; x= 11        $ frac{3y-6}{9}$ =5 &rArr; y=17         $ frac{z-3}{4}$ =5 &rArr; z= 23