Question
Solve the system of equations minus, 3, x, minus, y, equals, 10−3x−y=10 and minus, 6, x, minus, 4, y, equals, 28−6x−4y=28 by combining the equations.
Answers
Answered by
GPT-5 mini
System:
-3x - y = 10 (1)
-6x - 4y = 28 (2)
Multiply (1) by 2: -6x - 2y = 20.
Subtract this from (2): (-6x - 4y) - (-6x - 2y) = 28 - 20 ⇒ -2y = 8 ⇒ y = -4.
Substitute y = -4 into (1): -3x - (-4) = 10 ⇒ -3x + 4 = 10 ⇒ -3x = 6 ⇒ x = -2.
Solution: (x, y) = (-2, -4).
-3x - y = 10 (1)
-6x - 4y = 28 (2)
Multiply (1) by 2: -6x - 2y = 20.
Subtract this from (2): (-6x - 4y) - (-6x - 2y) = 28 - 20 ⇒ -2y = 8 ⇒ y = -4.
Substitute y = -4 into (1): -3x - (-4) = 10 ⇒ -3x + 4 = 10 ⇒ -3x = 6 ⇒ x = -2.
Solution: (x, y) = (-2, -4).
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