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 ：$\boxed{{\displaystyle x=9,y=12}}$