A linear equation involving two variables has an infinite number of solutions, all of which lie on the graph which makes a diagonal line. A second linear equation will also have its own infinite number of solutions.
When the two equations are combined into a system, there may be 1 coordinate that is common to both of the systems. This is located at the point of intersection of the two lines, and represents the solution to the entire system.
Once you find the solution, you can easily test whether it is the solution to the system by substituting the x and y values into both of the equations in the system. If it really is the solution, then it will make both equations true.
- p424 #1-4, #5ac #6, #7ac, #8-18 20 *23
Things you should be able to do after today:
- determine the solution for a system of linear equations graphically
- relate the coordinate for the solution to a linear system to the equations in the system