SOLUTION: Michelle earned a total of $549 in simple interest from two separate accounts. In an account earning 9% interest, Michelle invested $2,300 more than twice the amount she invested i

From the condition, you have these two equations

x = 2300 + 2y,           (1)   ("In an account earning 9% interest, Michelle invested $2,300 more than twice the amount 
                                 she invested in an account earning 1%.")
0.09x + 0.01y = 549      (2)   ("earned a total of $549 in simple interest from two separate accounts")


Modify the equations (the system) to the standard form.  On the way, multiply by 100 both sides in eq(2). You will get

 x - 2y = 2300,          (3)
9x +  y = 54900.         (4)


Multiply eq(4) by 2 (both sides), by keeping eq(3) without change. You will get

  x - 2y =   2300,       (5)
18x + 2y = 109800.       (6)


Now add eq(5) and eq(6). The terms "-2y" and "2y" will cancel each other, and you will get a single equation for x:

19x      = 2300 + 109800 = 112100  ====>  x =  = 5900.


Thus 5900 dollars were invested at 9%.

Then from eq(1),  2y = 5900 - 2300 = 3600.   Hence,  y =  = 1800.


Answer.  $5900 invested at 9%  and  $1800 invested at 1%.


Check.   0.09*5900 + 0.01*1800 = 549.   ! the solution is correct !