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Determining Whether an Ordered Triple is a Solution:
To evaluate whether the ordered triple is a common solution to the system of linear equations \left\{\begin{array}{l} x - y + z = 2 \ 2x - y - z = -6 \ 2x + 2y + z = -3 \end{array} ight., substitute the values , , and into each equation. Evaluating the first equation yields . Evaluating the second equation yields . Evaluating the third equation yields . Because the substitution produces true mathematical statements for all three equations, the ordered triple is confirmed as a valid solution to the overall system.
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Intermediate Algebra @ OpenStax
Ch.4 Systems of Linear Equations - Intermediate Algebra @ OpenStax
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