The problem describes a middle school where the total number of students last year was 440. This year, the number of boys decreased by 10%, and the number of girls increased by 5%, resulting in a total decrease of 14 students. We are asked to create a system of equations using $x$ to represent the number of boys last year and $y$ to represent the number of girls last year.

1. Problem Description

The problem describes a middle school where the total number of students last year was

4

4

0. This year, the number of boys decreased by 10%, and the number of girls increased by 5%, resulting in a total decrease of 14 students. We are asked to create a system of equations using $x$ to represent the number of boys last year and $y$ to represent the number of girls last year.

2. Solution Steps

First, we know that the total number of students last year was 440, so we have the equation:

$x + y = 440$

Next, we are told that the number of boys decreased by 10%, so the new number of boys is $x - 0.1x = 0.9x$. The number of girls increased by 5%, so the new number of girls is $y + 0.05y = 1.05y$. The total number of students decreased by 14, so the new total number of students is $440 - 14 = 426$. Therefore, we have the equation:

$0.9x + 1.05y = 426$

So the system of equations is:

$x + y = 440$

$0.9x + 1.05y = 426$

3. Final Answer

The system of equations is:

$x + y = 440$

$0.9x + 1.05y = 426$