Question

The sum of two numbers is 99 and the difference is 13. Use a system of two equations and two variables to solve and find the two
numbers.

Answer 1

Answer:

56 and 43

Step-by-step explanation:

(x+13)+x = 99

2x+13 = 99

2x = 99-13

2x = 86

x = 86/2

x = 43

Smaller number = 43

Larger number is 56

Check

56-43 = 13

56+43 = 99

Answer 2

Answer:

The two numbers are 43 and 56.

Step-by-step explanation:

Represent the numbers by x and y.

Then, according to the given information,

x + y = 99 and x - y = 13

Rewrite these two equations in a column:

x + y = 99

x -  y = 13

Solve this system of linear equations through elimination by addition/subtraction:

x + y = 99

x -  y = 13

---------------

2x = 112, so that x = 56

Next, find y by substituting 56 for x in either of the two equations:

56 - y = 13

This reduces to 43 - y = 0, or y = 43

The two numbers are 43 and 56.

Check:  Is the difference between 56 and 43 equal to 13?  YES

Is the sum of the numbers 56 and 43 equal to 99?  YES