Ernie deposited $4000 between two savings accounts. one account paid 4% simple interest and the other paid 2%. at the end of one year, ernie had earned $140 in interest for both accounts. how much money did ernie deposit in the account that paid 4% interest?

Let x represent the amount of $ in the 4% account and y in the 2% account.
Then x + y = $4000 (total savings).

Interest at 4% would be  x*0.04*1 = 0.04x, and
Interest at 2% would be  y*0.02*1 = 0.02y.

Then 0.04x + 0.02y = $140 interest, total.  

We must solve this system of linear equations.

Mult. 0.04x + 0.02y = $140 by 100 to remove the fractions:

4x + 2y = $14000       We already know that x + y = $4000, so y = $4000-x.

Then  4x + 2y = $14000 becomes  4x + 2($4000-X) = $56000.

Simplifying,                                     4x + $8000 - 2x = 14000.
                                                        2x                      = $6000
                                                          x     =     $3000 at 4%
                                                          y     =      $1000 at 2%