Formulate but do not solve the problem. Michael Perez has a total of $ 1855 on deposit with two savings institutions. One ( x ) pays interest at a rate of 5% /year, whereas the other ( y ) pays interest at a rate of 8% /year. If Michael earned a total of $ 122 in interest during a single year, how much does he have on deposit in each institution? ______= Â 122 _______= 1855 Write the system of equations corresponding to the augmented matrix using the variables x , y , and z . 8= Â _________ -4= __________ 3= _____________ Solution LET THE AMOUNT EARNING 5%INTEREST BE X $ AMOUNT EARNING 8% INTEREST = (1855 - X) $ Interest earned = 0.05 * X + 0.08 * ( 1855 - X) = 122 0.05X + 148.4 - 0.08X = 122 -0.03X = -148.4 +122 = -26.4 X = 26.4 / 0.03 = 880 $ 0.05 X 880 = 44 $ 0.08X(1855-880) = 78 $ Total = 122 $ B) 5y +3z = 8 x -y -5z = -4 5x +3z = 3 .