Three times one number added to another number is 39 . Twice the first number minus the other is 6 . What are the numbers?

Step 1 ：Let the first number be x and the second number be y. The given equations are:

Step 2 ：\(3x + y = 39\)

Step 3 ：\(2x - y = 6\)

Step 4 ：To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method. Add the two equations:

Step 5 ：\((3x + y) + (2x - y) = 39 + 6\)

Step 6 ：\(5x = 45\)

Step 7 ：Divide both sides by 5:

Step 8 ：\(x = \frac{45}{5}\)

Step 9 ：\(x = 9\)

Step 10 ：Substitute the value of x in the first equation:

Step 11 ：\(3(9) + y = 39\)

Step 12 ：\(27 + y = 39\)

Step 13 ：Subtract 27 from both sides:

Step 14 ：\(y = 39 - 27\)

Step 15 ：\(y = 12\)

Step 16 ：\(\boxed{x = 9, y = 12}\)