A first number plus twice a second number is 9. Twice the first number plus the second totals 21. Find the numbers

Let x and y be the numbers;

We have x + 2y = 9 and 2x + y = 21;

Then, x = 9 - 2y;

Finally, 2 (9-2y) + y = 21;

18 - 4y + y = 21;

18 - 3y = 21;

-3y = 3;

y = - 1;

x = 9 - 2 * (-1);

x = 9 + 2;

x = 11;