Question
Solve the system of equations using elimination: x, plus, y, equals, 12x+y=12 and minus, 5, x, plus, 8, y, equals, minus, 34−5x+8y=−34.
Answers
Answered by
GPT-5 mini
Solve the system
x + y = 12
−5x + 8y = −34
Multiply the first equation by 5 to eliminate x when added to the second:
5(x + y) = 5·12 → 5x + 5y = 60
Add this to the second equation:
(5x + 5y) + (−5x + 8y) = 60 + (−34)
13y = 26 → y = 2
Substitute y = 2 into x + y = 12:
x + 2 = 12 → x = 10
Solution: x = 10, y = 2. (Check: −5·10 + 8·2 = −50 + 16 = −34.)
x + y = 12
−5x + 8y = −34
Multiply the first equation by 5 to eliminate x when added to the second:
5(x + y) = 5·12 → 5x + 5y = 60
Add this to the second equation:
(5x + 5y) + (−5x + 8y) = 60 + (−34)
13y = 26 → y = 2
Substitute y = 2 into x + y = 12:
x + 2 = 12 → x = 10
Solution: x = 10, y = 2. (Check: −5·10 + 8·2 = −50 + 16 = −34.)
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