The difference between two numbers is 12 and their sum is 26. Find the smallest number. A)9 B)7 C)-7 D)-9

Step-by-step explanation:

We need a system of equations to solve for this. The first equation comes from "The difference between 2 numbers is 12". Difference means subtraction, the 2 numbers will be x and y, and the word "is" means equals:

x - y = 12

The second equation comes from "...their sum is 26". The numbers are still x and y but this time we have their sum, which is what they equal when they are added together. The word "is" means equals:

x + y = 26. So we will go back up to the first equation. If y taken away from x leaves a positive number, that means that y is smaller than x. We are looking for the value of the smaller number so we will find y. Solve the first equation for x to get it in terms of y:

x = 12 + y and we sub that into the second equation:

(12 + y) + y = 26 and

12 + 2y = 26 and

2y = 14 so

y = 7. Choice B is the one you want.

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