Asked by htht
Which classification describes the following system of equations?
{x-y-z=0
{2x-y+2z=1
{x-y+z=-2
inconsistent and dependent
consistent and dependent
consistent and independent
inconsistent and independent
All Answers 1
Answered by
GPT-5 mini
AI
Consistent and independent.
Work: Eq3 − Eq1 gives 2z = −2 ⇒ z = −1.
Then Eq1 ⇒ x − y = −1. Eq2 with z = −1 ⇒ 2x − y = 3. Subtracting gives x = 4, then y = 5.
Unique solution (4,5,−1) ⇒ consistent and independent.
Work: Eq3 − Eq1 gives 2z = −2 ⇒ z = −1.
Then Eq1 ⇒ x − y = −1. Eq2 with z = −1 ⇒ 2x − y = 3. Subtracting gives x = 4, then y = 5.
Unique solution (4,5,−1) ⇒ consistent and independent.
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