Section 3-1: Graphing Systems of Equations Pages 126-132 in textbook
Objectives I can solve systems of equations by graphing them. I can identify the 3 types of solutions to a system of equations
System of Equations When you have 2 or more equations to solve at one time, we call this a system of equations. The solution set to the system is where the graphs intersect. When will 2 lines intersect? If they have different slopes. Let’s look at an example.
Given the following system of equations, solve by graphing. x + y = 6 and 3x – 4y =4 One of the easiest ways to graph is to get these into slope intercept form: x + y = 6 becomes y = -x + 6 3x – 4y = 4 -4y = -3x + 4 y = ¾ x -1
Lines intersect at one point: consistent & independent
BIG PICTURE The solution to a system of equations is where the graphs cross! The solution is always Ordered Pair Format! There are 3 types of solutions –One Solution (Ordered Pair) –No Solution –Infinite Solutions