1. Graphing Systems of Equations
Objective:
Formulate systems of linear equations in two unknowns to solve problems.

2. What is a System of Linear Equations?
A system of linear equations is simply two or more linear equations using the same variables.
We will only be dealing with systems of two equations using two variables, x and y.
If the system of linear equations is going to have a solution, then the solution will be an ordered pair (x , y) where x and y make both equations true at the same time.
If the lines are parallel, there will be no solutions.
If the lines are the same, there will be an infinite number of solutions.

3. If the lines cross once, there
will be one solution.
If the lines are parallel, there
will be no solutions.
If the lines are the same, there
will be an infinite number of
solutions.

4. Graphing to Solve a Linear System
Let's summarize! There are 4 steps to solving a linear system using a graph.
Step 1: Put both equations in slope - intercept form.
Solve both equations for y, so that each equation looks like
y = mx + b.
Step 2: Graph both equations on the same coordinate plane.
Use the slope and y - intercept for each equation in step 1. Be sure to use a ruler and graph paper!
Step 3: Estimate where the graphs intersect.
This is the solution! LABEL the solution!
Step 4: Check to make sure your solution makes both equations true.
Substitute the x and y values into both equations to verify the point is a solution to both equations.

5. Solving Systems of Equations by Graphing
Suppose you are going on vacation and leaving your dog in a kennel. The Bowowery charges $ 25 per day, which includes a one-time grooming treatment. The Poochpad charges $ 20 per day, and a one-time fee of $30 for grooming.