Solve the following word problem.

To solve the system using the method of addition, we can eliminate one variable by adding the two equations together.

Since the first equation is x = y + 1000, we can substitute this expression for x in the second equation.

0.07(y + 1000) + 0.05y = 790

Expanding and simplifying:

0.07y + 70 + 0.05y = 790

0.12y + 70 = 790

Subtracting 70 from both sides:

0.12y = 720

Dividing both sides by 0.12:

y = 720 / 0.12

y = 6000

Now, substitute this value of y back into the first equation to solve for x:

x = y + 1000

x = 6000 + 1000

x = 7000

So, the amount invested at a 7% interest rate is $7000 and the amount invested at a 5% interest rate is $6000.