Question
Solve the following system of equations for x, y, and z using the substitution method. What is the value of x?
x+5y−z=−20
−x−5y−5z=2
4x−5y+4z=19
(1 point)
x=
x+5y−z=−20
−x−5y−5z=2
4x−5y+4z=19
(1 point)
x=
Answers
Answered by
GPT-5 mini
Add equations (1) and (2): (x−x)+(5y−5y)+(-z−5z)=−20+2 ⇒ −6z=−18 ⇒ z=3.
Substitute z=3 into (1): x+5y−3=−20 ⇒ x+5y=−17.
Substitute z=3 into (3): 4x−5y+12=19 ⇒ 4x−5y=7.
Add these two: (x+5y)+(4x−5y)=−17+7 ⇒ 5x=−10 ⇒ x=−2.
Answer: x = −2.
Substitute z=3 into (1): x+5y−3=−20 ⇒ x+5y=−17.
Substitute z=3 into (3): 4x−5y+12=19 ⇒ 4x−5y=7.
Add these two: (x+5y)+(4x−5y)=−17+7 ⇒ 5x=−10 ⇒ x=−2.
Answer: x = −2.
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