SOLUTION: Solve the system of linear equations. x-4y+z=11 4x+y-2z=5 x-4y+2z=9 A.The unique solution to the system is ​(Type an exact answer in simplified​ form.) B. A

Algebra ->  Expressions-with-variables -> SOLUTION: Solve the system of linear equations. x-4y+z=11 4x+y-2z=5 x-4y+2z=9 A.The unique solution to the system is ​(Type an exact answer in simplified​ form.) B. A      Log On


   

Question 1086861: Solve the system of linear equations.
x-4y+z=11
4x+y-2z=5
x-4y+2z=9

A.The unique solution to the system is
​(Type an exact answer in simplified​ form.)
B.
All three equations describe the same plane.
C.
The system has infinitely many solutions. The solution described in terms of variable z is=
D.
There is no solution to the system.
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
x-4y+z=11 [1]
4x+y-2z=5 [2]
x-4y+2z=9 [3]
Subtract [1] from [3]:
This gives z = -2
Substitute this value into [2] and solve for y in terms of x:
4x + y + 4 = 5
y = 1 - 4x
Use either [1] or [3] to solve for y:
x - 4(1 - 4x) - 2 = 11
17x = 17
x = 1
Thus y = 1 - 4*1 = -3
Ans A. The unique solution is 1, -3, -2