The larger of two numbers is 1 more than 3 times the smaller. the diffrence is between 8 time the smaller and 2 tmies the larger is 10 find the numbers

Let the two numbers be x and y, with y being larger than x.
Then y=3x+1.
Also, 8x-2y= 10.

The first equation has already been solved for y.  Substitute 3x+1 for y in the second equation:

8x-2(3x+1)=10, or 8x - 6x - 2 = 10,  or  2x  = 12 and x = 6.

If x = 6, then by the first equation y must be 3(6)+1, or 19.

The numbers are 6 and 19.