Transcript
- 1. Slide 1: Solving a system of equations by graphing. Slide 2: What is a system of equations? It’s solving 2 equations at the same time by locating the point of intersection. The easiest method for finding the point of intersection is by graphing the lines on a coordinate plane. For the example shown on this slide, the two lines intersect at the point (1,1) therefore the point (1,1) is the solution to the system. Slide 3: How do I graph the lines? In order to graph each line, you must solve each equation for y, if necessary, so the equation is written in slope-intercept form y=mx+b. You will then graph each line on the same coordinate plane by plotting the y-intercepts and then counting the rise and run for the slope. Slide 4: How do I find the solutions? Once both lines are graphed on the same coordinate plane, you will need to locate the point of intersection which is where the 2 lines cross each other. This ordered pair is the solution to the system and can be checked by substituting the point back into the given equations to be sure it makes both equations true. Slide 5: What if the lines don’t cross? Sometimes, the graph that results from the system will be of 2 parallel lines that will never intersect. In this case, since there is no point of intersection, the system would have No Solution. Slide 6: What if the lines are the same? You may also get a system whose graph results in only one line. This means the 2 equations have the same graph and one line is graphed on top of the other. This means they intersect at all points, not just one so this system has infinitely many solutions or All Solutions.