We start by assigning variables to represent their ages
Let Lisa's age be represented by l and Patrick's age be represented by p
First part of the question states that the sum of their ages is 38
Mathematically;
[tex]l\text{ + p = 38 }\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(i_{})[/tex]The difference of their ages is 8, and since Patrick is older, we have the equation as;
[tex]\begin{gathered} p\text{ - l = 8} \\ \\ \text{This means} \\ \\ p-8\text{ = l }\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots..(ii) \end{gathered}[/tex]Now substitute equation ii into i; we have
[tex]\begin{gathered} p\text{ - 8 + p = 38} \\ \\ 2p\text{ - 8 = 38} \\ \\ 2p\text{ = 38 + 8} \\ \\ 2p\text{ = 46} \\ \\ p\text{ = }\frac{46}{2} \\ \\ p\text{ = 23} \end{gathered}[/tex]