Chapter 13
Streamlining Systems, Managing Variables
In This Chapter
Taking down two-equation systems with substitution and elimination
Breaking down systems with more than two equations
Graphing systems of inequalities
Forming and operating on matrices
Putting matrices into simpler forms to solve systems of equations
When you have one variable and one equation, you can almost always solve the equation. Finding a solution may take you some time, but it is usually possible. When a problem has two variables, however, you need at least two equations to solve; this set of equations is called a system. When you have three variables, you need at least three equations in the system. Basically, for every variable present, you need a separate unique equation if you want to solve for it.
For an equation with three variables, an infinite number of values for two variables would work for that particular equation. Why? Because you can pick any two numbers to plug in for two of the variables in ...
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