solve using elimination: u+v+w=6, u+2v+2w=11, 2u+3v-4w=3.....i keep getting the wrong answers according to wolf ram and i am not sure why

Question

campbell_st · Answer

label your equations (1), (2), (3) and reduce the 3 equations to 2 equations in 2 unknowns.. 

Eliminate u

Equation (1) - Equation (2) gives    -v -w = -5             (4)

2 x Equation (1) - Equations(3)  gives  -v + 6w = 9      (5)

Eliminate v

-1 x Equation (4) + equation (5) = 7w = 14
 
Substitute to get the other pronumerals. 


My solution is u =1, v = 3 and w = 2

phi · Answer

u+v+w=6, u+2v+2w=11, 2u+3v-4w=3

just the coefficients, in order u v w constant

1   1   1   6
1   2   2  11
2   3  -4  3

multiply the top row by -1 and add to the 2nd row
( we add -1 -1 -1 -6 to the 2nd row)
1   1   1  6
0   1   1  5
2   3  -4  3

multiply the top row by -2 and add to the 3rd row
(we add -2 -2 -2 -12 to the 3rd row)
1   1   1   6
0   1   1   5
0   1  -6  -9

multiply the 2nd row by -1 and add to the 3rd row
(add 0 -1 -1 -5 to the 3rd row)
1   1   1    6
0   1   1    5
0   0  -7  -14

backsolve (start at the bottom)
w= -14/-7 = 2
v + 2= 5, v= 3
u+3+2=6, u = 1

anonymous · Answer

Answer :
    u = 1
    v= 3
     w = 2