Solve this system of equations using the addition or subtraction method. Check. x - 2y = 14 x + 3y = 9 Simultaneous equations got you baffled? Relax! You can do it! Think of the adding or subtracting method as temporarily eliminating one of the variables to make your life easier. Systems of Equations may also be referred to as simultaneous equations. Simultaneous means being solved at the same time. Lets look at three examples using the addition or subtraction method for systems of equations: 1. Solve this system of equations and check: x - 2y = 14 x + 3y = 9 a. First, be sure that the variables are lined up under one another. In this problem, they are already lined up. x - 2y = 14 x + 3y = 9 b. Decide which variable (x or y) will be easier to eliminate. In order to eliminate a variable, the numbers in front of them (the coefficients) must be the same or negatives of one another. Looks like x is the easier variable to eliminate in this problem since the xs already have the same coefficients. x - 2y = 14 x + 3y = 9 c. Now, in this problem we need to subtract to eliminate the x variable. Subtract ALL of the sets of lined up terms. (Remember: when you subtract signed numbers, you change the signs and follow the rules for adding signed numbers.) x - 2y = 14 -x - 3y = - 9 - 5y = 5 d. Solve this simple equation. -5y = 5 y = -1 e. Plug y = -1 into either of the ORIGINAL equations to get the value for x. x - 2y = 14 x - 2(-1) = 14 x + 2 = 14 x = 12 f. Check: substitute x = 12 and y = -1 into BOTH ORIGINAL equations. If these answers are correct, BOTH equations will be TRUE! x - 2y = 14 12 - 2(-1) = 14 12 + 2 = 14 14 = 14 (check!) x + 3y = 9 12 + 3(-1) = 9 12 - 3 = 9 9 = 9 (check!)
Posted on: Fri, 21 Nov 2014 03:41:50 +0000
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