Find the value of x, y and z, so as to satisfy the equations given below:
x + y +z = 12; x + y – z = 6; x – y + z = 4 

Options
a) x = 5, y = 4, z = 3
b) x = 5, y = -4, z = -3
c) x = 5, y = -4, z = 3
d) x = 5, y = 4, z = -3

Solution

As per question
x + y + z = 12 ___________ (1)
x + y – z = 6 _____________ (2)
x – y + z = 3 _____________ (3)
Equation (1) – (2)
(x + y + z) – (x + y – z) = 12 – 6
x + y + z – x – y + z = 6
2z = 6
z = 3
Equation (1) – (3)
(x + y + z) – (x – y + z) = 12 – 4
x + y + z – x + y – z = 8
2y = 8
y = 4

Put value of y and z in equation (1)
x + y + z = 12
x + 4 + 3 = 12
x + 7 = 12
x = 12 – 7
x = 5
x = 5 , y = 4 , z = 3

Answer: x = 5 , y = 4 , z = 3