Algebra II Workbook For Dummies, 2nd Edition

Chapter 11

Solving Systems of Linear Equations

In This Chapter

Solving systems of two and three linear equations using algebraic methods

Using Cramer’s rule to solve systems of two equations

Applying systems of equations to breaking fractions apart

Linear equations have variables that don’t exceed the power of one. For example, the equation 2x + 3y – z = 0 is linear. A system of linear equations can contain any number of equations and any number of variables. But the only systems that have the possibility of having a unique solution are those where you have at least as many equations as variables. When looking for solutions of systems of equations, you try to get one numerical value for x, one for y, one for z, and so on. Another type of solution is a rule or generalization relating the values of the variables to one another.

In this chapter, you use substitution and elimination to solve the linear systems. You also use Cramer’s rule as an alternative when fractional answers get nasty. Finally, you decompose fractions, which means breaking fractions into simpler fractions. Linear equations come in very handy when decomposition is desired (bet you never expected to read that decomposition ...