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Unformatted text preview: 41 Systems of Equations (two variables)Consider the following systemof equations:y = x + 2 y = x + 4Our job: find a point (pair (x,y)) that satisfies bothequationsIf we graph these equations, we get:describe the point that satisfies both equationswhat are its coordinates?does that point, in fact, satisfy both equations?graphical method(just shown):can be an effective way, using a graphing calculatorwe will concentrate on systematic, algebraicmethods41p. 1y4x4y = x + 2y = x + 4Solving systems by eliminationExample:x + y = 4x  y = 1Strategy: add the two equations in order to "eliminate" one of the variablesx + y = 4+x  y = 1_____________________2x = 5You now have one equation with one unknown.Solve it for x, substitute in 1 or 2 and solve for y.Example:3x + 3y = 152x + 6y = 22Mere adding won't eliminate. We multiply each equation by an appropriate constant so adding willeliminate (eitherx or y):2: 6x + 6y = 303:6x  18y = 66___________________________________12y = 36y = 3etc....
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 Spring '11
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 Systems Of Equations, Equations

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