Question

Solve the following equations by reduction method: 

x+ y+z = 6,

3x-y+3z = 10

5x+ y-4z = 3 

Answer 1

Given equation in matrix form as 

`[(1,1,1),(3,-1,3),(5,1,-4)] [(x),(y),(z)] = [(6),(10),(3)]`

R₂  → R₂ - 3 and R₃  → R₃ -5 R₁ 

`[(1,1,1),(0,-4,0),(0,-4,-9)] [(x),(y),(z)] = [(6),(-8),(-27)]`

R₁  → R₃ - R₂ 

`[(1,1,1),(0,-4,0),(0,0,-9)] [(x),(y),(z)] = [(6),(-8),(-19)]`

∴ x + y + z = 6         ........(i)

∴ -4y = -8                ........(ii)

∴ -9z = -19               ........(iii)

From (iii) , z = `19/9`

From (ii) , y = 2

From (i),  x + 2 + `19/9` = 6

`=> "x" + 37/9 = 6`

`=> "x" = 17/9`

∴ `"x" = 17/9` , y = 2 , z = `19/9`