Awoman invests a total of $20,000 in two accounts, one paying 2.5% and the other paying 8% simple interest per year. her annual interest is $830. how much did she invest at each rate?

Let's have a variable for each rate
x = account 1 (2.5% rate of interest)
y = account 2 (8% rate of interest) 

The formulas we need are: 
0.025x + 0.08y = 830 (amount of interest paid) 
x + y = 20 000 (combined amount invested) 

To solve we will use substitution (isolate for one variable and plugging into the other formula): 
x + y = 20 000
x = 20 000-y

0.025x + 0.08y = 830
0.025(20 000-y) + 0.08y = 830
500-0.025y+0.08y=830
500+0.055y=830
0.055y=330
y=6000

Now that we know y (the 2nd account) = $6000 we need to find x. We do this by using the previous formula.
x = 20 000-y
x=20 000 - 6000
x=14000

She invested $14 000 at a 2.5% interest rate and $6 000  at a 8% interest rate.

*Notes:
the percentages were converted into decimal form
you check your answer by plugging the numbers back into the 2 formulas we made