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

Algebra/Trig ReviewIn this graph the red plane is the graph of 2x− y− 2z=− 3, the green plane is thegraph of x+ 3y+ z = 1 and the blue plane is the graph of 5x− 4y+ 3z= 10 . You cansee from this figure that the three planes do appear to intersect at a single point. It is asomewhat hard to see what the exact coordinates of this point. However, if we couldzoom in and get a better graph we would see that the coordinates of this point are(0, − 1, 2) .2. Determine where the following two curves intersect.2 2x + y = 132y = x −1SolutionIn this case we’re looking for where the circle and parabola intersect. Here’s a quickgraph to convince ourselves that they will in fact. This is not a bad idea to do withthis kind of system. It is completely possible that the two curves don’t cross and wewould spend time trying to find a solution that doesn’t exist! If intersection points doexist the graph will also tell us how many we can expect to get.© 2006 Paul Dawkins 34http://tutorial.math.lamar.edu/terms.aspx