Section 3.5: Solving Systems by Elimination Worksheet 3.5
We've talked about several ways of solving systems: graphically, with a table, and numerically (with a computer).
We also talked about substitution, which is an algebraic method.
Question: Are there other ways?
Example: Let's solve a system using the elimination method.
$$\left\{\begin{array}{l}-3x-5y=-1\\x+2y=1\\\end{array}\right\}$$
The Method of Elimination: An Algebraic Method
Step 0: If there are fractions, clear them.
Step 1: Multiply either one or both equations so that the coefficients on either $x$ or $y$ are opposites.
Step 2: Add both equations together. One variable should disappear (the one with opposite coefficients from previous step.)
Step 3: You have an equation in 1 variable which you will solve. (Either $x=$NUMBER or $y=$NUMBER).
Step 4: Plug the NUMBER you get into any of the two original equations. This will give you another equation in the other variable. Solve this equation to get the other number.
Step 5: Check your work!
Example
Solve the following system by elimination.
$$\left\{\begin{array}{l}-x+2y=-4\\3x+3y=-3\\\end{array}\right\}$$
Question: But what happens if there are infinitely many or no solutions?