Set up the system of equations and then solve it by using an inverse matrix.

A trust account manager has $2,000,000 to be invested in three different accounts. The accounts pay 6%, 8%, and 10%, and the goal is to earn $174,000 with the amount invested at 10% equal to the sum of the other two investments. To accomplish this, assume that x dollars are invested at 8%, y dollars at 10%, and z dollars at 6%. Find how much should be invested in each account to satisfy the conditions.