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Formulate a system of equations from the description. Let [tex]\( a \)[/tex] be the first number and [tex]\( y \)[/tex] be the second number. Do not solve.

The sum of two numbers is 62. The second number is 5 more than twice the first number.

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Given:
- The sum of two numbers is 62.
- The second number is 5 more than twice the first number.

Let [tex]\( a \)[/tex] be the first number.
Let [tex]\( y \)[/tex] be the second number.

System of equations:
[tex]\[ a + y = 62 \][/tex]
[tex]\[ y = 2a + 5 \][/tex]



Answer :

GinnyAnswer
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.

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