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Unformatted text preview: 4-1 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, algebraicmethods4-1p. 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 = 30-3:-6x - 18y = -66___________________________________-12y = -36y = 3etc....
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