On two investments totaling $13,500, Peter lost 3% on one and earned 5 % on the other. If his net annual receipts were $319, how much was each investment?

X = amount of 3% loss investment
y = amount of 5% gain investment

x + y = 13,500 {the two investments total $13,500}
-0.03x + 0.05y = 319 {3% loss on one and 5% gain on other, receipt is $319}

x = -y + 13,500 {subtracted y from each side of first equation}

-0.03(-y + 13,500) + 0.05y = 319 {substituted (-y + 13,500), in for x, into second equation}
0.03y - 405 + 0.05 = 319 {used distributive property}
0.08y - 405 = 319 {combined like terms}
0.08y = 724 {added 405 to each side}
y = 9050 {divided by 0.08}

x = -y + 13,500 {from equation above}
x = -9050 + 13,500 {substituted 9050 in for y}
x = 4450 {added}

The 3% loss investment was $4450
The 5% gain investment was $9050