Checkpoint: Solutions to Systems of Equations with Three Variables Solutions

Determine whether the ordered triple is a solution to the system of equations. Explain. (1.5, 3, –1.5)

$3 x - 2 y - z = 0 x + y - z = 6 10 x - y = 12$

$3 (1.5) - 2 (3) - (- 1.5) = 0 ✓ (1.5) + (3) - (- 1.5) = 6 ✓ 10 (1.5) - (3) = 12 ✓$

The ordered triple is a solution because all equations are true when the values are substituted into the system.

Note

Q: Suppose the final equation was replaced with 10x – z = 12. Will the given ordered triple still be the solution? Explain.
A: No, the ordered triple will not be a solution because 10(1.5) – (–1.5) is 16.5, not 12.