Question

Use back-substitution to solve the system of linea {(x-2y+4z=8),(y=2),(y+z=1):}

Answer 1

To solve the system of linear equations using back-substitution, substitute the given value of y into the other equations and solve for the remaining variables.

Step-by-step explanation:

To solve the system of linear equations using back-substitution:

1. Start by using the second equation, y = 2, to substitute for y in the other two equations.
2. Substitute y = 2 into the third equation, y + z = 1, to solve for z.
3. Once you have found the value of z, substitute it back into the second equation, y = 2, to double check your solution for y.
4. Finally, substitute the values of y and z back into the first equation, x - 2y + 4z = 8, and solve for x.

The solution to the system of linear equations is (x, y, z) = (6, 2, -1).