Write and solve equations here. Let the two numbers be x and y.
Then x + 3y = 24, and 5x + 3y = 36. Solve this system of linear equations.
Note that the first equation can easily be solved for x. Then x = 24 - 3y. Subbing 24 - 3y for x in the 2nd eq'n, we get:
5(24 - 3y) + 3y = 36, or 120 - 15y + 3y = 36
-12y = 36 - 120, or -12y = -84
-84
Solving for y: y = ------- = 7
-12
If y is 7, then x is 24 - 3(7). Simplifying, x = 24 - 21 = 3.
Then the solution is (3, 7).
By all means insert 3 for x and 7 for y in either of the original equations. If that equation comes out to be true, you'll know your solution is correct.