Let x represent the amount earned by James per year. We were told that Lin earns $3200 more per year than James. This means that the amount earned by Lin per year is
x + 3200
Together they earn $82,060. This means that
x + 3200 + x = 82060
3200 + 2x = 82060
2x = 82060 - 3200 = 78860
x = 78860/2
x = 39430
James earns $39430 per year
Lin earns 39430 + 3200 = $42630 per year