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

Define the two numbers

Let the first number be x.
Let the second number be y.


Form equations and solve x and y

x + 2y = 14 (1)
2x + y = 31  (2)


Equation (1) x 2

2x + 4y = 28  (1a)


Equation (1a) - 2

3y = 28 - 31
3y = -3
y = -1


Substitute y = -1 into (1)

x + 2(-1) = 14
x -2 = 14
x = 14 + 2
x = 16


x =16, y = -1

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