The sum of two numbers is 10. The larger number is 4 times the smaller number. What are the two numbers?

Question

Let x = the smaller number.

Let y = the larger number.

Which two equations represent the system for this word problem?

Equation 1:
Equation 2:

Answer 1

Let's define the two equations based on the problem statement:

1. The sum of the two numbers is 10:
   \[ x + y = 10 \]

2. The larger number is 4 times the smaller number:
   \[ y = 4x \]

Thus, the two equations representing the system for this word problem are:

Equation 1: \( x + y = 10 \)
Equation 2: \( y = 4x \)