Answer:
The solution to the system of equation is:
x = -2
y = -1
z = -1
Step-by-step explanation:
Given the system of equations:
4x - 3y - 6z = 1 .............................................(1)
x - y - 6z = 5 .................................................(2)
6x - y = -11 .....................................................(3)
Subtract (2) from (1) to eliminate z
3x - 2y = -4 ...................................................(4)
Multiply (4) by 2 and subtract (3) from the result to eliminate x
(4) * 2: 6x - 4y = -8
- (3)
-3y = 3
Divide both sides by -3
y = 3/(-3) = -1 ......................................................(5)
Multiply (3) by 2 and subtract (4) from the result to eliminate y
(3) * 2: 12x - 2y = -22
- (4)
9x = -18
Divide both sides by 9
x = -18/9 = -2 ........................................................(6)
Put x = -2 and y = -1 in (2) to find z
-2 - (-1) - 6z = 5
-1 - 6z = 5
-6z = 5 + 1
-6z = 6
Divide both sides by -6
z = 6/(-6) = -1 .........................................................(7)
Therefore, x = -2, y = -1, and z = -1(