Final answer:
To solve the triangular system using back-substitution, you solve the equations starting from the last one and then substitute the found values back into the preceding equations. The solution is x = -3.5, y = 1, and z = 8.
Step-by-step explanation:
To use back-substitution to solve the given triangular system, you start by solving the equations in reverse order. Here is the step-by-step process:
- Start with the last equation, which is the simplest one. From the equation 1/2z = 4, you can solve for z by multiplying both sides by 2 to get z = 8.
- Next, move to the second equation, which is 2y - z = -6. Since we now know that z = 8, we can substitute this value into the equation to get 2y - 8 = -6. Adding 8 to both sides gives us 2y = 2, and dividing by 2, yields y = 1.
- Finally, substitute both y and z back into the first equation, which is 4x + 3z = 10. Since y is not in this equation and z = 8, we substitute z to get 4x + 3(8) = 10, which simplifies to 4x + 24 = 10. Subtracting 24 from both sides gives us 4x = -14, and dividing by 4 yields x = -3.5.
Therefore, the solution to the system is x = -3.5, y = 1, and z = 8.