Answer:
(x, y, z) = (2, -4, 3)
Explanation:
It is convenient to let an appropriate calculator reduce the augmented matrix to reduced row-echelon form. The rightmost column in that form is the solution vector [x, y, z].
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If you want to solve this by hand, you can perform the following row operations to reduce the augmented matrix as shown in the attachment.
r1 ← r2 +r3; r2 ← (r2 +r3)/7 . . . . use this matrix for the next row replacement
r3 ← (r3 -r1 -4·r2)/11 . . . . . . . . . . use this matrix for the next row replacement
r1 ← r1 -2·r2 +5·r3
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r1, r2, r3 refer to rows 1, 2, 3, respectively. The indicated multiplication and division are scalar operations, operating on each individual term in the row.
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Additional comment
Most graphing calculators have matrix solving functions. Apps are available for phone and tablet that will do this, and there are online websites that will reduce an augmented matrix as well.