The sum of two integers is 36, and the difference is 6. What is the smaller of the two numbers?
Let x = the ?rst integer and let y = the second integer. The equation for the sum of the two integers is x + y = 36, and the equation for the difference between the two integers is x - y = 6. To solve these through the elimination method, merge such as terms vertically and the variable of y cancels out.
x + y = 36
x - y = 6
This results in: 2x = 42, so x = 21
Substitute the value of x into the ?rst equation to get 21 + y = 36. Sub- tract 21 from both sides of this equation to obtain an answer of y = 15.