A first plus twice a second number is one. twice the first number plus the second totals fourteen.

First Number = 9

Second Number = - 4

Step-by-step explanation:

Let the first number be "x" and the 2nd number be "y"

First number PLUS twice 2nd is 1, so we can write:

x + 2 y = 1

Twice First number PLUS the 2nd number is 14, so we can write:

2x + y = 14

We can write:

y = 14 - 2x

We put this into 1st equation and solve for x:

x + 2y = 1

x + 2 (14 - 2x) = 1

x + 28 - 4x = 1

-3x = - 27

x = 9

And now y:

y = 14 - 2 (x)

y = 14 - 2 (9)

y = 14 - 18

y = - 4

First Number = 9

Second Number = - 4