Select the set of equtions that represents the following equation.The sum of two numbers is 38, and their difference is 26 more than the smaller number what are the two numbers?

a.)x+y=38;y-x=x+26
b.)2x=38;61=x+26
2y=38;61=x-26
x+y=38;x-y=26-x

To solve this problem, we need to translate the given information into a set of equations. Let's break down the problem step by step:

1. "The sum of two numbers is 38": Let's assume the two numbers are x and y. The sum of x and y should equal 38, so the equation would be x + y = 38.

2. "Their difference is 26 more than the smaller number": The difference between two numbers can be found by subtracting one from another. In this case, we need to compare the smaller number (let's assume it is x) with the difference, which is 26 more than x. Therefore, the equation would be y - x = x + 26.

Now let's evaluate each option to see which set of equations represents the problem correctly:

a.) x + y = 38; y - x = x + 26

This option represents the problem correctly. The first equation states that the sum of the two numbers is 38. The second equation represents that their difference is 26 more than the smaller number (x).

b.) 2x = 38; 61 = x + 26, 2y = 38; 61 = x - 26

This equation set seems incorrect as it does not align with the information given. The first and third equations are incorrect because they do not represent the sum or difference of the two numbers. The second equation is not related to the problem and seems unrelated to finding the two numbers.

c.) x + y = 38; x - y = 26 - x

This represents part of the problem, but the second equation is incorrect. The difference between the two numbers should be 26 more than the smaller number, not 26 minus the smaller number.

Therefore, the correct set of equations is a.) x + y = 38; y - x = x + 26.

To find the two numbers, you can solve these two equations simultaneously using algebraic methods such as substitution or elimination.