2.1 Systems of Equations Mr. Anderson Pre Calculus Falconer Central High School Falconer, NY

Terminology A system of equations consists of m equations having a total of n different variables. These equations are given together and grouped together to be solved together. We say that “we have m equations in n unknowns”. Example

4 methods to do this 1) Substitution To use this method, we solve one equation for one of the variables, and then substitute into the other equation. The purpose for this is to get one equation in one variable.

Example 1 Notice that both equations are already solved for “y”. Substitute the second equation into the first. Now we have one equation in one variable. Solve for the variable – in this case “x”. Use any of the given equations to find values for all other variables.

Method 2 Graphically We can solve each equation for a variable (probably “y”) and then graph all equations to find their intersection. Note that this only works well for equations that are linear in y.

Method 3 Cancellation Cancel one of the variables by subtracting one equation from another. *Note that you might have to do some multiplication first.

Example 2 Notice that the coefficients on the “y” terms are the same. Subtract one equation from the other. Finish solving for the variable, and don’t forget to find a value for the other variable (not shown).

Example 3 Check this out…

Example 4

Homework Pg. 59 # 1-10 [2], [4] do all problems both ways.