The sum of two numbers is 59 and the difference is 7. what are the numbers

To solve this problem, let's set up a system of equations.  To do this, we can let one of the two unknown numbers be represented by the variable x and the other unknown number be represented by the variable y.  We know that the difference between the two variables is 7 and the sum of the two variables is 59, which allows us to create the two equations below:

x - y = 7

x + y = 59

To solve this system of equations, we are going to use linear combination, which means simply adding the two left sides of the equations together and adding the two right sides of the equations together.  Because the first equation has a -y term on the left side and the second equation has a +y term on the left side, these are going to cancel out, leaving us with:

2x = 66

To solve this equation, we must get the variable x alone on the left side of the equation by dividing both sides of the equation by 33, giving us:

x = 33

To solve for the other number, we must plug this known value for x into one of our original equations, as follows:

x + y = 59

33 + y = 59

To solve for the variable y, we must subtract 33 from both sides of the equation to get the variable y alone.  This operation gives us:

y = 26

Therefore, the two numbers are 33 and 26.

Hope this helps!