Systems of Equations and Inequalities: Systems of Equations with Three Variables

Think & Click: Problem Solving Using Systems of Three Equations

Now, you try. Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.

In my pocket, I have coins which total $1.35. They are a total of 9 coins which are nickels, dimes and quarters. There are twice as many quarters as there are dimes. How many of each coin do I have?

N + D + Q = 9
Q = 2D
0.05N + 0.10D + 0.25Q = 1.35

a three by three matrix with the first row: 1, 1, 1; the second row: 0, negative 2, 1; and the third row: 0.05, 0.10, 0.25; times a three by one matrix with terms N, D, Q, equals a three by one matrix with terms 9, 0, 1.35

3 nickels, 2 dimes, 4 quarters

I am thinking of three numbers. If I add all the numbers together, the result will be 30. If I multiply the first number by 5 and subtract the second number, the result will be equal to the third number. The third number is three times the first number. What are the numbers?

A + B + C = 30
5A – B = C
C = 3A

a three by three matrix with the first row: 1, 1, 1; the second row: 5, negative 1, negative 1; and the third row: negative 3, 0, 1; times a three by one matrix with terms A, B, C, equals a three by one matrix with terms 30, 0, 0

A = 5, B = 10, C = 15

Review Worksheet

Complete the review worksheet for this section before taking the quiz. Download the review worksheet, complete the questions, and then download the answer key to check your work. Make sure to ask your teacher any questions.