Final answer:
To find the number of miles Erica ran this week and last week, we can set up a system of equations based on the given information. Solving this system of equations, we find that Erica ran 26 miles this week and 16 miles last week.
Step-by-step explanation:
To solve this problem, we need to create a system of equations based on the given information. Let x represent the number of miles Erica ran this week, and y represent the number of miles she ran last week.
Based on the given information, we can set up two equations:
1. x = 2y - 6 (Erica ran 6 less than 2 times the number of miles she ran last week)
2. x + y = 42 (The total number of miles Erica ran this week and last week is 42)
We can now solve this system of equations to find the values of x and y.
Substituting the value of x from equation 1 into equation 2, we get: (2y - 6) + y = 42. Simplifying this equation gives us 3y - 6 = 42. Adding 6 to both sides, we have 3y = 48. Dividing both sides by 3, we find that y = 16.
Substituting the value of y into equation 1, we get x = 2(16) - 6, which simplifies to x = 26.
Therefore, Erica ran 26 miles this week and 16 miles last week.