The interest on an investment varies directly as the rate of interest. If the interest is $47 when the interest rate is 4%, find the interest when the rate is
5.5%.

2a - 5b = 1
3a + 5b = 14

Let's solve this system using elimination. Add the equations together to cancel the b-terms, then solve for a.

    2a - 5b = 1
   3a + 5b = 14
+
    5a - 0 = 15
         5a = 15
           a = 3

Next, plug 3 for a into either of the equations and solve for b.

  2a - 5b = 1
2(3) - 5b = 1
    6 - 5b = 1
       - 5b = -5
           b = 1

Lastly, check all work by plugging both values for their respective variables.

     2a - 5b = 1
2(3) - 5(1) = 1
         6 - 5 = 1  --  This is true

     3a + 5b = 14
3(3) + 5(1) = 14
         9 + 5 = 14  --  This is true

The solution to the system of equations is (3, 1).