Question

Solve the following equations by method of reduction: 

x-y + z = 4,

2x + y - 3z = 0,

x + y + z = 2

Answer 1

x-y + z = 4,

2x + y - 3z = 0,

x + y + z = 2

`[[1,-1,1],[2,1,-3],[1,1,1]][[x],[y],[z]]=[[4],[0],[2]]`

`R_2-2R_1 and R_3-R_1`

`[[1,-1,1],[0,3,-5],[0,2,0]][[x],[y],[z]]=[[4],[-8],[-2]]`

`x-y+z=4`   ....(1)

`3y-5z=-8` ....(2)

`2y=-2`           ....(3)

y=-1

By equation (2)

`–3 – 5z = – 8`
`–5z = –5`
`z = 1`

By equation (1)

`x + 1 + 1 = 4`
`x = 2`
Ans : `x = 2, y = –1, z = 1`