Question

Find the solution to the system of equations represented by the matrix shown below. 3 -1 7 53 1 7 1 61 9 1 1 67​

Answer 1

Answer:

  (x, y, z) = (6, 7, 6)

Step-by-step explanation:

Maybe your matrix is ...

  $\left[\begin{array}{ccc|c}3& -1& 7& 53\\ 1& 7& 1& 61\\ 9& 1&1&67\end{array}\right]$

A calculator can tell you the solution is ...

  (x, y, z) = (6, 7, 6)

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For systems of equations in more than 2 variables the third variable can be defined in terms of the other two (as for solution by substitution). This can be substituted into the remaining equations to obtain two equations in two unknowns. That solution can then be used to find the value of the third variable. The attachment shows application of this method.

We used the last equation to define z, then used that definition in the first two equations. The same approach can be used for an algebraic solution.

The solution is (x, y, z) = (6, 7, 6).