Solve for the variables in these simultaneous equations: 3x - 2y - z = 23, 5x + y + 3z = 23 and 4x + y - 5z = -18 ?

To solve these simultaneous equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From the first equation:
3x - 2y - z = 23
z = 3x - 2y - 23

Substitute z into the second equation:
5x + y + 3(3x - 2y - 23) = 23
5x + y + 9x - 6y - 69 = 23
14x - 5y = 92
14x = 5y + 92
x = (5y + 92) / 14

Substitute z into the third equation:
4x + y - 5(3x - 2y - 23) = -18
4x + y - 15x + 10y + 115 = -18
-11x + 11y = -133
11y = 11x - 133
y = x - 133 / 11

Now, substitute the expressions for x and y back into the equation for z:
z = 3((5y + 92) / 14) - 2y - 23
z = (15y + 276) / 14 - 2y - 23
z = (15(x - 133 / 11) + 276) / 14 - 2(x - 133 / 11) - 23

Therefore, the solution to the simultaneous equations is:
x = (5y + 92) / 14
y = x - 133 / 11
z = (15(x - 133 / 11) + 276) / 14 - 2(x - 133 / 11) - 23