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

Algebra/Trig ReviewDon’t forget the “ ± ” in the solution!2 22 2 5x+ y =2y= 5−2xy2 21= 5 − 22( x )2 25y =± −x22Solving Systems of Equations1. Solve the following system of equations. Interpret the solution.2x− y− 2z=−3x+ 3y+ z =−15x− 4y+ 3z= 10SolutionThere are many possible ways to proceed in the solution process to this problem. Allwill give the same solution and all involve eliminating one of the variables andgetting down to a system of two equations in two unknowns which you can thensolve.Method 1The first solution method involves solving one of the three original equations for oneof the variables. Substitute this into the other two equations. This will yield twoequations in two unknowns that can be solve fairly quickly.For this problem we’ll solve the second equation for x to get.x=−z−3y−1Plugging this into the first and third equation gives the following system of twoequations.2( −z−3y−1)− y− 2z=−35( −z−3y−1)− 4y+ 3z= 10Or, upon simplification−7y− 4z=−1−19y− 2z= 15Multiply the second equation by -2 and add.−7y− 4z=−138y+ 4z=−3031y= −31© 2006 Paul Dawkins 32http://tutorial.math.lamar.edu/terms.aspx