Seven times the first number plus six times the second number equals 31. Three times the first number minus ten times the second number is 29

Question

What are the 2 numbers? explain or show your reasoning.

Answer 1

Let x and y be the 2 numbers. The wording of the problem translates into

7x + 6y = 31

3x - 10y = 29

This is a system of 2 linear equations in 2 unknowns x and y, which you can solve by substitution, elimination, matrix methods, or Cramer's rule. For example, solve for y in terms of x in the top equation. Plug that into y in the bottom equation. That gives an equation in x only. Solve it for x, and then plug the result into the top equation, which gives an equation in y only. Solve it for y, and you are done.