A man invests $5,200, part at 4% and the balance at 3%. If his total income for the two investments is $194, how much money did he invest at

4% of X + 3% of Y = 194            and             X+Y=5200  multiply by 4

0.04X+0.03Y=194  multiply by 100

4X+3Y=19400    (1)                       and              4X+4Y=20800   (2)

(2) - (1)

4X-4X+4Y-3Y=20800-19400

Y=$1400

X=$5200-$1400 = $3800

(This is based on simple interest)