-4x - 5y - z = 18 -----------------------------(1)
-2x - 5y - 2z = 12 --------------------------------(2)
-2x + 5y + 2z = 4 ----------------------------------(3)
We will eliminate the y in equation (1) and (2)
To do that, subtract equation (2) from (1)
-2x + z =6 --------------------------------(4)
Similarly, eliminate y in equation (2) and (3)
To do that, Add equation (2) and equation (3)
-4x = 16---------------------------(5)
From equation (5) divide both-side of the equation by -4
x = -4
substitute x =-4 into equation (4) and solve for z
-2(-4) + z = 6
8 + z =6
subtract 8 from both-side of the equation
z = 6 - 8
z=-2
substitute the value of x=-4 and z=-2 into equation (1) and solve for y
-4(-4) -5y -(-2) = 18
16 -5y + 2 = 18
18 - 5y = 18
subtract 18 from both-side of the equation
-5y =0
Divide both-side by -5
y=0
Therefore,
x= -4 y=0 and z=-2