Systems of Linear Equations in Algebra II
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