Question

A first number plus twice a second number is 14. twice the first number plus the second totals 31. find the numbers.

Answer 1

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Define the two numbers
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Let the first number be x.
Let the second number be y.

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Form equations and solve x and y
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x + 2y = 14 ------------------ (1)
2x + y = 31 ------------------ (2)

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Equation (1) x 2
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2x + 4y = 28  ---------------(1a)

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Equation (1a) - 2
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3y = 28 - 31
3y = -3
y = -1

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Substitute y = -1 into (1)
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x + 2(-1) = 14
x -2 = 14
x = 14 + 2
x = 16

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Answer: x =16, y = -1
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