Math Mammoth Systems of Linear Equations

103 pages
(includes answers)

Sample pages (PDF)
Contents
Solving Systems of Equations by Substitution
Applications, Part 1
Speed, Time, and Distance Problems

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Math Mammoth Systems of Linear Equations is a worktext that covers how to analyze and solve pairs of simultaneous linear equations. This means students analyze and solve systems of linear equations that only contain two variables.

The first lesson, Equations with Two Variables, is optional. It reinforces the idea that a point on a line satisfies the equation of the line, and thus prepares the way for the main topics in the book.

First, students learn to solve systems of linear equations by graphing. Since each equation is an equation of a line, this is a simple technique, but it has its limitations, thus, algebraic solution methods will be taught also, in later lessons.

In the next lesson, we look at the number of solutions that a system of two linear equations can have. The three possible situations are easy to see based on the graphs of the equations: one solution (the lines intersect in one point), no solutions (lines are parallel), or an infinite number of solutions (the lines are the same).

In the next lesson, students learn the algebraic method of solving systems of equations by substitution. This is a straightforward technique; however, one has to be careful not to make simple mistakes. The lesson has some practice problems where students practice finding errors in solutions.

The next lesson, Applications, Part 1, has a variety of word problems that students can now solve using a system of equations. After that, students learn another algebraic method for solving systems of equations: the addition or elimination method. This is useful when the coefficients of the variables are such that you can easily find their least common multiple. Students also practice solving more complex systems, where the equations first have to be transformed and simplified, or include fractions.

Then it is time for more word problems, in the lesson Applications, Part 2. One lesson is devoted to problems about speed, time, and distance, and another for mixtures and comparisons. Making a chart is very helpful in these situations.

The book ends with a review lesson. The answers are appended.

The PDF version of this book can be filled in on a computer, phone, or tablet, using the annotation tools found in many PDF apps. See more.