Question

The number of solutions of the system of equations 2x + y - z = 7, x - 3y + 2z = 1 and x + 4y - 3z = 5 is

(a) 0 

(b) 1

(c) 2 

(d) 3

Answer 1

Correct Option: (a) 0

Explanation:

Given,

2x + y - z = 7 ...(i)

x - 3y + 2z = 1

and x + 4y - 3z = 5 ...(iii)

Multiplying (i) by 2 and then adding (i) and (ii), we get

5x - y = 15 ...(iv)

Multiplying (i) by 3 and then subtracting (iii) from (i), we get

5x - y = 16 ...(v)

Eqs. (iv) and (v) shows that they are parallel and so solution does not exist.