A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote. They wrote a total of 46 songs.

Question

Which system of equations models this situation if the drummer wrote `d` songs and the guitarist wrote`g` songs? solve it and tell me why

Answer 1

The system of equations that models this situation is:

1) g = 2d - 8
2) g + d = 46

To solve this system of equations, we can substitute the expression for g from the first equation into the second equation:

2d - 8 + d = 46
3d - 8 = 46
3d = 54
d = 18

Now that we have found the number of songs the drummer wrote, we can substitute this value back into the first equation to find the number of songs the guitarist wrote:

g = 2(18) - 8
g = 28

Therefore, the drummer wrote 18 songs and the guitarist wrote 28 songs.

This system of equations models the situation because it establishes the relationship between the number of songs the drummer and the guitarist wrote. The first equation relates the number of songs the guitarist wrote to the number of songs the drummer wrote, while the second equation states that the total number of songs they wrote was 46. By solving these equations simultaneously, we can determine the number of songs each band member wrote.