Using a system of equations, it is found that the numbers with the desired sum and difference are given by:
\(x = 3\frac{4}{8}, y = 1\frac{1}{8}\)
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are x and y. Initially applying the conversion from mixed to fraction, the system is:
\(x + y = \frac{36}{8} \rightarrow y = \frac{36}{8} - x\)
\(x - y = \frac{18}{8}\)
Since \(y = \frac{36}{8} - x\):
\(x = \frac{18}{8} + y\)
\(x = \frac{18}{8} + \frac{36}{8} - x\)
\(2x = \frac{54}{8}\)
\(x = \frac{54}{16}\)
\(x = \frac{27}{8}\)
Then y is given by:
\(y = \frac{36}{8} - x = \frac{36}{8} - \frac{27}{8} = \frac{9}{8}\)
Now we apply the conversion to mixed numbers, as 27 divided by 8 has quotient 3 and remainder 4, and 9 divided by 8 has quotient and remainder 1, hence:
\(x = 3\frac{4}{8}, y = 1\frac{1}{8}\)
More can be learned about a system of equations at https://brainly.com/question/24342899