1. Solving Linear Systems of Equations - Graphing Method
Recall that to solve the linear system of equations in two variables ...
we need to find the value of x and y that satisfies both equations. In this presentation the Graphing Method will be demonstrated.
Consider the system of equations ...

2. Sketch a graph of the first equation ...
Each point on the graph of the function satisfies the equation of the function ...
(x,y)

3. Now add a sketch of the second function to the graph.
Each point on the graph of this function satisfies the equation of the function ...
(x,y)

4. Now consider the point of intersection of the two graphs ...
Since this point is on both graphs, it must be a solution point for both equations!
We only need to determine the coordinates of the point to have the solution to the system of equations.
(1,3)
It appears that the point is ...

5. Let x = 1 and y = 3 in each equation.
The ordered pair (1, 3) is now confirmed as the solution to the system of equations.
(1,3)

6. Summary:
1) Graph both functions on the same coordinate
plane.
2) Determine the point of intersection for the two
graphs.
3) Substitute the coordinates of the point into
both equations to make sure it is a solution
to the system.

7. While the graphing method is helpful in gaining a visual understanding of solving systems of equations, it is not very practical for solving systems whose solutions are not integers. For example, the solution (3/7, - 2/9) is not likely to be found by this method.
When approximate solutions are desired, the graphing calculator can be used very effectively with this method.

8. Example: use a graphing calculator to find the solution to the following system (nearest hundredth).
Place each equation into y = f(x) form:

9. Enter the functions into Y1 and Y2 on the calculator ...
Use a ZOOM|ZStandard window ...
Use CALC|Intersect to find the point of intersection ...
The solution is

10. END OF PRESENTATION