If the system of linear equations given by x + y + z = 3 , 2 x + 2 y - z = 3 , x + y - z = 1 is consistent and if x 0 , y 0 , z 0 is a solution, then 2 x 0 + 2 y 0 + z 0 =

Step-by-step solution

Given, x + y + z = 3       . . . i 2 x + 2 y - z = 3     . . . i i x + y - z = 1     . . . i i i Adding, we get x + y = 2     . . . i v Substituting this value of x + y in i , we get z = 1 Now, if x 0 , y 0 , z 0 is the solution then x 0 + y 0 = 2   &   z 0 = 1 . Then, 2 x 0 + 2 y 0 + z 0 = 2 x 0 + y 0 + z 0 = 2 × 2 + 1 = 5 .