Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig ReviewOn occasion you will want the complex solutions and on occasion you won’t want thecomplex solutions. You can usually tell from the problem statement or the type ofproblem that you are working if you need to include the complex solutions or not. Inthis case we were after where the two curves intersected which implies that we areafter only the real solutions.3. Graph the following two curves and determine where they intersect.2x= y −4y−8x= 5y+28SolutionBelow is the graph of the two functions. If you don’t remember how to graphx= f y go back to the Graphing and Common Graphs sectionfunction in the form ( )for quick refresher.There are two intersection points for us to find. In this case, since both equations areof the form x= f( y)we’ll just set the two equations equal and solve for y.2y −4y− 8 = 5y+282y −9y− 36 = 0( y+ 3)( y− 12)= 0The y coordinates of the two intersection points are then y = − 3 and y = 12 . Now,plug both of these into either of the original equations and solve for x. I’ll use the line(second equation) since it seems a little easier.First, y = − 3 .Now, y = 12.x = 5( − 3)+ 28 = 13x = 5( 12)+ 28 = 88© 2006 Paul Dawkins 36http://tutorial.math.lamar.edu/terms.aspx