The system of equations is solved by expressing z in terms of x from the first equation, substituting into the second to find x, then z, and finally substituting x and z into the third to find y. The solution is the ordered triple (-2, 5, 1).
To solve the system of equations -2x + z = 5, 3x + 2z = -4, and -x + 4y - 2z = 16, we can use the method of substitution or elimination. Here's a step-by-step explanation for solving it:
- First, solve the first equation for z to get z = 2x + 5.
- Next, substitute z into the second equation, resulting in 3x + 2(2x + 5) = -4. Solve for x to find x = -2.
- With x known, substitute it back into z = 2x + 5 to find z = 1.
- Finally, substitute x and z into the third equation -x + 4y - 2z = 16 to find 4y = 16 + 2 + 2 = 20 and thus y = 5.
In conclusion, the ordered triple that represents the solution of the system is (-2, 5, 1).