Afirst number plus twice a second number is 1. twice the first number plus the second totals 11. find the numbers.

First number : x
second number : y

x + 2y = 1
2x + y = 11

multiply the first equation by 2...
2x + 4y = 2
2x + y = 11

subtract them

3y = -9
y = -3

use one of the equations to find x.
x + 2y = 1
x + 2(-3) = 1
x - 6 = 1
x = 7

So the first number is 7 and the second number is -3.

Hope this helped!! :)