$5900 was invested at the 10% rate.
To solve this problem, you have to write then solve a system of equations.
Let x be the amount at 10% and y be the amount at 7%.
We can write the following 2 equations.
x + y = 9500
0.1x + 0.07y = 842
Now, you can solve the equations by elimination, substitution or graphing.
Either way, the solution is (5900, 3600).