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Chapter 11

Systems of Linear Equations

A linear equation consists of variable terms whose exponents are always the number 1. When you have two variables, the equation can be represented by a line. With three terms, you can draw a plane to describe the equation. More than three variables is indescribable, because there are only three dimensions. When you have a system of linear equations, you can look for the values of the variables that work for all the equations in the system — the common solutions. Sometimes there’s just one solution, sometimes many, and sometimes there’s no solution at all.

The Problems You’ll Work On

In this chapter on systems of linear equations, you’ll see the following:

 Determining the point of intersection of two lines

 Finding a single point of intersection of three planes

 Writing expressions for multiple solutions of systems

 Writing systems in the echelon form or reduced row echelon form

 Decomposing fractions using systems of linear equations

What to Watch Out For

Don’t let common mistakes trip you up; watch for the following ones when working with systems of linear equations:

 Trying to eliminate more than one variable when solving a system

 Distributing negative numbers incorrectly over several terms

 Writing the coordinates of ordered pairs and ordered triples in the incorrect positions

 Placing the incorrect numerator over its denominator when decomposing fractions

Solving Systems of Two Linear Equations

651–660 Solve the system of two linear equations for x and y.

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Performing Row Operations on Linear Equations

661–665 Interpret the operation notation; then perform that operation on the equations.

661. when

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Solving Systems of Equations with Row Echelon Form

666-675 Write each system of equations in the row echelon form and substitute back to solve the system.

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Using Reduced Row Echelon Form to Solve Systems

676–680 Write each system of equations in the reduced row echelon form and identify the solution.

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Solving Systems of Linear Equations

681–690 Solve the system of equations.

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Decomposing Fractions Using Systems of Equations

691–695 Perform decomposition of the fraction using a system of equations.

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