Can someone explain how to do this in detail! (number 1)

Start by calling the number of home runs Peter hit 'P' and the number Alice hit "A'. 

We know that "Altogether, they 18 home runs" so .

We laso know that "Peter hit twice the difference of the the number of home runs Alice hit and 6. So:

Now we can substitute the second equation into the first:



And solve for A:




Alice hit 10 home runs.

Now we can plug this known value into the first equation and solve for P:




Peter hit 8 home runs.

To check, we can use the other equation that we didn't backsubstitute into:




CHECK