Certainly! Let's break down the problem step-by-step to formulate the system of equations:
1. Assign variables:
- Let [tex]\( a \)[/tex] represent the first number.
- Let [tex]\( y \)[/tex] represent the second number.
2. Translate the given information into equations:
- First Piece of Information:
The sum of the two numbers is 62.
This can be written mathematically as:
[tex]\[
a + y = 62
\][/tex]
- Second Piece of Information:
The second number is 5 more than twice the first number.
This can be written mathematically as:
[tex]\[
y = 2a + 5
\][/tex]
3. Combine the two equations into a system of equations:
[tex]\[
\begin{cases}
a + y = 62 \\
y = 2a + 5
\end{cases}
\][/tex]
So, the system of equations based on the given problem is:
[tex]\[
\begin{cases}
a + y = 62 \\
y = 2a + 5
\end{cases}
\][/tex]
This is the desired system of equations formulated from the given description.
