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.