Linear programing problem that is not seeming to be a linear programming problem

Carl bought two pieces of lnd for a total of $225,000. When he sold the first plot of land, he made a profit of 12%. When he sold the second plot of land, he lost 8%. His total profit from selling the two pieces of land was $4,000. Find how much he paid for each piece of land.

Let x = the price of the first plot of land
Let y = the price of the second plot of land

x + y = 225000
1.12x + 0.92y = 229000

-1.12x - 1.12y = -252000
1.12x + 0.92y = 229000

-0.20y = -23000
y = $115000

x + y = 225000
x = 225000 - 115000
x = $110000


CHECK:

1.12x + 0.92y = 229000
123200 + 105800 = 229000
229000 = 229000