the sum of the two numbers is 13 and the difference is five what are the two numbers?

Answer 1

Since the sum (addition) of two numbers is 13, we have to solve for A + B = 13. We also know the difference (subtraction) of two numbers is 5, we have to solve for A - B = 5.

A + B = 13

A - B = 5

By combining these two equations, the left side of the equation has A + A = 2A, while B - B cancels each other out. On the right side of the equation, we have 13 + 5 = 18. We now have 2A = 18. In order to get A by itself, we must divide by 2. In order to keep our equation balanced, whatever we do to the left side we must also do to the right side. 2A / 2 = A, and 18 / 2 = 9. Therefore, A = 9.

Now we go back to the original equations and substitute for 9 for A. Since 9 + B = 13, then B would equal 4. You could subtract 9 from both the left side and right side to keep them balanced, leaving you with B = 4. You can confirm your answer by solving the second equation and substitute 9 for A again. Since 9 - B = 5, then B would equal 4. You can double check your answer by substituting A=9 and B=4 into both equations to verify they now have true statements. 9 + 4 = 13, and 9 - 5 = 4, so we have indeed solved correctly.

Answer 2

X + y = 13

X-y=5

Aodds them together

2x= 18

X=9

9 and 4