Answer
x = -3
y = 2
z = -2
Explanation
We are asked to use elimination method to solve the three equation simultaneous equation
3x + 4y - z = 1
3x - y - 4z = -3
x + 3y - 3z = 9
To use elimination method, we first make z the subject of formula from the first equation
3x + 4y - z = 1
3x + 4y - 1 = z
z = 3x + 4y - 1
We can then substitute this value of z into the remaining two equations
3x - y - 4z = -3
x + 3y - 3z = 9
z = 3x + 4y - 1
3x - y - 4(3x + 4y - 1) = -3
3x - y - 12x - 16y + 4 = -3
3x - 12x - y - 16y = -3 - 4
-9x - 17y = -7 ......... equation *
x + 3y - 3z = 9
x + 3y - 3(3x + 4y - 1) = 9
x + 3y - 9x - 12y + 3 = 9
x - 9x + 3y - 12y = 9 - 3
-8x - 9y = 6 ........... equation **
We can then have these two equations together
-9x - 17y = -7 ......... equation *
-8x - 9y = 6 ........... equation **
We can then solve these two equation simultaneous equation easily
Solving simultaneously, we obtain that
x = -3 and y = 2
We can then solve for z
z = 3x + 4y - 1
z = 3(-3) + 4(2) - 1
z = -9 + 8 - 1
z = -2
Hope this Helps!!!