Anne invested $10 000 for 1 year. she invested part at 8% per year and the rest at 10% per year. the total interest earned for 1 year was $940. how much did she invest at each rate?

Let us say she invested two amounts, "a" at 8% interest and "b" at 10%, per annum

for one year, she got $940

we dunno what "a" and "b" are, but we know, they total 10,000,  or 
a + b = 10,000

whatever they're

we also know, their interest yield was 940 in total
so... 8% of a, or 8/100 * a or 0.08a
added to
10% of b, or 10/100 * b or 0.10b
they add up to 940

thus 0.08a + 0.10b = 940
thus  

solve for "a", to see how much was invested at 8%

what about "b"? well, b = 10,000 - a