ANSWER
The two numbers are,
[tex]9 \: \: and \: \: 12[/tex]
EXPLANATION
Let the numbers be
[tex]x \: \: and \: \: y[/tex]
where x is the smaller number.
We were told that the sum of the two numbers is 21.
This means that, if we add the two numbers, we should get 21.
This implies that,
[tex]x + y = 21 - - (1)[/tex]
We were also told that, the larger number is 6 less than twice the smaller number.
Since x is the smaller number, twice the smaller number will be,
[tex]2x[/tex]
The greater number being 6 less than twice the smaller number, means we should subtract 6 from twice the smaller number before we can get the greater number,
This implies that,
[tex]y = 2x - 6 - - (2)[/tex]
We substitute equation (2) in to equation (1) to obtain,
[tex]x + 2x - 6 = 21[/tex]
This implies that,
[tex]3x = 27[/tex]
Divide through by 3 to obtain,
[tex]x = 9[/tex]
We substitute the value of x into equation 2 to find y.
[tex]y = 2 \times 9 - 6[/tex]
[tex]y = 18 - 6[/tex]
[tex]y = 12[/tex]
