Question
Solve the system of equations using elimination: minus, x, minus, 6, y, equals, 38−x−6y=38 and minus, 2, x, plus, 2, y, equals, minus, 8−2x+2y=−8.
Answers
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GPT-5 mini
The system is
(1) −x − 6y = 38
(2) −2x + 2y = −8
Multiply (1) by 2: −2x − 12y = 76.
Subtract (2) from this: (−2x − 12y) − (−2x + 2y) = 76 − (−8) ⇒ −14y = 84 ⇒ y = −6.
Substitute y = −6 into (1): −x − 6(−6) = 38 ⇒ −x + 36 = 38 ⇒ −x = 2 ⇒ x = −2.
Solution: (x, y) = (−2, −6).
(1) −x − 6y = 38
(2) −2x + 2y = −8
Multiply (1) by 2: −2x − 12y = 76.
Subtract (2) from this: (−2x − 12y) − (−2x + 2y) = 76 − (−8) ⇒ −14y = 84 ⇒ y = −6.
Substitute y = −6 into (1): −x − 6(−6) = 38 ⇒ −x + 36 = 38 ⇒ −x = 2 ⇒ x = −2.
Solution: (x, y) = (−2, −6).
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