Answer :
Let x be the principal of the first loan, and y be the principal of the second loan, then, we can set the following system of equations:
[tex]\begin{gathered} x+y=12,000, \\ 0.08x+0.09y=1,010. \end{gathered}[/tex]Solving the first equation for x, we get:
[tex]x=12,000-y\text{.}[/tex]Substituting the above result in the second equation, we get:
[tex]0.08(12,000-y)+0.09y=1,010.[/tex]Solving the above equation for y, we get:
[tex]\begin{gathered} 960-0.08y+0.09y=1,010, \\ 0.01y=1,010-960, \\ 0.01y=50, \\ y=5000. \end{gathered}[/tex]Substituting y=5000, in x=12,000-y, we get:
[tex]x=12,000-5000=7000.[/tex]Answer:
The principal of the 8% interest loan was $5000, and the principal of the other loan was $7000.