A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Fi

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A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Find the numbers

Let the first number be a and the second number be b. We have:

1. a + 2b = 7
2. 2a + b = 23

Rearrange (1) into (3)
(3) a = 7 - 2b

Substitute (3) into (2):
2(7 - 2b) + b = 23

Multiply through:
14 - 4b + b = 23

Combine like terms:
14 - 3b = 23

Subtract 14 from each side:
-3b = 9

Divide each side by -3
b = -3

Substitute this into (3)
a = 7 - 2b
a = 7 - 2(-3)
a = 7 + 6
a = 13

(a, b) = (13, -3)