In Algebra II, 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 find 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.

When solving systems of linear equations, watch out for these mistakes:

  • Forgetting to change the signs in the factored form when identifying x-intercepts

  • Making errors when simplifying the terms in f(–x) applying Descartes’ rule of sign

  • Not changing the sign of the divisor when using synthetic division

  • Not distinguishing between curves that cross from those that just touch the x-axis at an intercept

  • Graphing the incorrect end-behavior on the right and left of the graphs