Question

Please explain on how to get the solution for each variable please

Answer 1

By algebraic handling we find that the unique solution of the system of linear equations is: (x, y, z) = (- 2, 4, 3). (Correct choice: A)

What is the nature of a system of linear equations?

If the system of equations has no solutions, then the determinant of the dependent coefficients of the system of linear equations must be zero. Let see:

$D = \left|\begin{array}{ccc}1&1&1\\4&-1&-8\\-1&-1&7\end{array}\right|$

This determinant can be determined by Sarrus' rule:

D = (1) · (- 1) · (7) + 4 · (- 1) · 1 + (- 1) · 1 · (- 8) - (- 1) · (- 1) · 1 + 4 · 1 · 7 - 1 · (- 1) · (- 8)

D = - 7  - 4 + 8 - 1 + 28 - 8

D = 16

The system of linear equations have at least one solution. This system has only one solution any of the three equations is not a function of the other two. By algebraic handling we find that the unique solution of the system is: (x, y, z) = (- 2, 4, 3).

To learn more on systems of linear equations: brainly.com/question/19549073

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