Since you have two unknowns, you must formulate 2 equations in order to solve the system. Let x be the numbers of dimes and y be the number of quarters. The equations are:
x + y = 61
y = x + 3
Since a dime is 1/10 of a dollar and a quarter is 1/4 of a dollar,
(1/10)x + (1/4)y = 10.90
We made 3 equations. The system is overspecified. Let's just use the first two equations and apply it to the third for verification.
x + (x + 3) = 61
Solving for x,
x = 29
y = 29 + 3 = 32
Verifying,
(1/10)(29) + (1/4)(32) = 10.90
Hence, there are 29 dimes and 32 quarters.
