The sum of two numbers is 3.1. Twice the large number is 7 more than 3 times the smaller number. What are the numbers?

Let the two numbers be x and y where x is greater than y.

So;

x + y = 3.1 ... (i)

2x - 3y = 7 ... (ii)

This forms a set of simultaneous equations (i) and (ii)

Solving the simultaneous equations by elimination;

We multiply (i) by 2 and (ii) by 1 to get:

2x + 2y = 6.2 ... (i)

2x - 3y = 7 ... (ii)

Subtracting (i) - (ii) we get;

5y = - 0.8

y = - 0.8/5 = - 0.16

x = 3.1 - - 0.16 = 3.26

The numbers are 3.26 and - 0.16.