In one baseball season, peter hit twice the difference of the number of homeruns alice hit and 6. altogether, they hit 18 homeruns. how many homeruns did each player hit that
season?

In order to solve this problem, the approach should be formulating equations such that they form a system of linear equations. Let's start by assigning variables. Let x be the number of homeruns made by Peter, and y be the number of homeruns made by Alice. Therefore,

x = 2(y - 6)

This is the equation for the relationship between Peter's and Alice's hits. The second equation would be the sum of their hits:

x + y = 18

These are the two independent equations in order to solve the two unknowns, x and y. Substituting the first equation into the second equation,

2(y - 6) + y = 18
2y - 12 + y = 18
3y = 18 + 12
3y = 30
y = 10

Using y=10 to the first equation:
x = 2(10 - 6)
x = 8

Therefore, Peter made 8 homeruns, while Alice made 10 homeruns for a total of 18.