Systems of Equations and Inequalities: Systems of Equations

Systems of equations are used to solve real world problems.

Joe has a pocketful of nickels and dimes. He has 30 coins all together and they total $2.45. We can write two equations with this information.

Using N to represent nickels and D to represent dimes, we can write the equation for the number of coins:

N + D = 30

Since nickels are worth $0.05 and dimes are worth $0.10, we can write the equation for the value of the coins:

0.05N + 0.10D = 2.45

We now have a system of two equations and two variables.

N + D = 30
0.05N + 0.10D = 2.45

We can use any of the three methods, substitution, elimination, or matrices, to solve this system of equations.

In this example, I will use substitution. The first equation can be solved for N and substituted into the second equation.

N = 30 – D
0.05(30 – D) + 0.10D = 2.45
1.5 – 0.05D + 0.10D = 2.45
1.5 + 0.05D = 2.45
0.05D = 0.95
D = 19

N + 19 = 30
N = 11

Joe has 11 nickels and 19 dimes in his pocket.