SolvingSystems.Graphing

Return to Chapter 7: Solving Systems of Equations

**Graphing Method** This is the basic way of solving a system of linear equations. All you do is graph the equations and see where they intersect. Graphing in slope intercept form (y=mx+b) is (in my opinion) the easiest way to solve a system of linear equations, I always convert standard from into slope intercept form. // To graph in slope intercept form, //** mark the Y intercept (b) on the graph and use the slope to make the line. ** // To graph with standard form, //** find the X and Y intercepts and mark them on the graph. To find the X and Y intercepts, substitute 0 in for X to find the Y intercept, then substitute 0 in for Y to find the X intercept. **

**If you use a graph, a solution of linear equations is where the two equations intersect on the graph. Since they both share that point, it is a solution for both of them.**

**There are 3 possible solutions for a linear system.** Intersecting lines have a standard ordered pair solution. This is called a // consistent, independent system //   Parallel lines have // no solution. //   Coinciding (lines that overlap completely) have an // infinite number of solutions //, but they __have__ to be on the lines. //In the graph above, if the a point does not have 3 for the x value, it is not a solution.// //In the graph above, the solution must have a slope of 1 and a Y intersect// //of about 1/2.//

y=2x+4 y=x+3 You graph the equations and find where they intersect.
 * To solve a system of linear equations by graphing, you really only need to know how to graph.**



Looking at the graph, we can see that the lines intersect at (-1,2) From here you can check your answer. 2=2(-1)+4 is correct 2=-1+3 is also correct, so the answer is (-1,2)

** Solving systems of linear equations on a graphing calculator. ** To solve systems graphing on a Casio calculator, press menu and press graph or 5. //It has to be in slope intercept form// .From there just type in the equations and press draw. After they are drawn, press F5 (G-solve) and press ISCT and the x and y value that come up is your solution. **// If you can't view it, or it looks weird, press Shift F3 and change the x and y min to -10, the x and y max to 10, and the x and y scale to 1. //**

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