Algebra II: 1001 Practice Problems For Dummies (+ Free Online Practice). Mary Jane Sterling

      645.

Sketching the Graphs of Hyperbolas

       646–650 Sketch the graph of the hyperbola.

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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

      662. when

663. when

      664. when

      665. when

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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675.

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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