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Classnotes Systems by Linear Combination 2-23/2-24 Algebra II CP The 3rd and last method for solving systems of 2 equations in 2 variables is called Linear Combination. This method will work for all systems, and is less work than substitution. The goal of Linear Combination is to get either the x variable or the y variable to cancel out. In order for this to happen, you must leave your 2 equations in standard form and stacked over one another. Examine the coefficients of the terms and decide if x or y will eliminate from the original system OR if x or y will eliminate if you multiply one equation by a factor to force the terms to be equal opposites. Once this is in place, “add” the other columns of variables and constants – thus solving for one of your two variables. Example: x + 5y = 33 4x + 3y = 13 Notice that neither the x column nor the y column will eliminate if you add straight down the columns as they are currently written. If however, you multiply the top equation by -4, the x column would then eliminate. Thus, the new system would look like: now, “add” each column -4x -20y = -132 4x + 3y = 13 -17y = -119 y=7 now solve for the value of the y-coordinate It is your choice as to which of the original equations you substitute the value y = 7 into to get the value for x. I am going to use the 1st equation: x + 5(7) = 33 x + 35 = 33 subtract 35 from both sides x = -2 Therefore the ordered pair solution for this system is ( -2, 7) There are more examples in your textbook in section 3.2 Classwork for the day is p. 152 #23-34 I have tentatively set the chapter 3 test for next Wednesday, March 2