Answer
No solution
Work Step by Step
We start by simplifying the equation by eliminating x so we can work with 2 variables.
To do so, we multiply -x + 6y + z = 4 by 3 to get:
-3x + 18y + 3z = 12 and add
3x -2y + 2z = 5 *the first equation
We are left with the equation 16y + 5z = 17
We then get our second two-variable equation by subtracting the first equation
3x - 2y + 2z = 5 from the third equation
3x + 14y + 7z = 20 to get
-16y -5z = -15
When we add these two equations
-16y -5z = -15
16y + 5z = 17 together, we get
0 = 2, which is impossible.
Thus, the system is inconsistent and has no solution.
