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Solving Equations Numerically Figure 4.1a Rename the independent variable x if necessary. For Figure 4.1a, Set up the table. Set up the first column for the independent variable, x, by setting a minimum integer value, 0, and increments of 1 for integers. 2nd TBLSET 1 0 ENTER (Minimum number in the table is 0.) (Independent variable values are increasing by 1.) Set the calculator to perform the operations automatically. ENTER ▼ Technology 4.1 1 of 3

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Solving Equations Numerically Figure 4.1b For Figure 4.1b, Set up the second column to be the expression on the left side by entering the left expression of the equation, 2x + 3, in Y1. 5 ENTER + 3+2Y= Set up the third column to be the expression on the right side by entering the right expression of the equation, x + 5, in Y2. Technology 4.1 X,T, ,n 2 of 3

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Solving Equations Numerically Figure 4.1c For Figure 4.1c, View the table. Move beyond the screen to view additional rows by using the up and down arrows. The solution is the x-value that results in equal Y1 and Y2 values. The solution of 2x + 3 = x + 5 is 2 because 7 = 7. 2ndTABLE Technology 4.1 3 of 3

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Solving Equations Graphically Solve 2x + 3 = x + 5 graphically. Figure 4.4a Rename the independent variable x if necessary. Enter the expression on the left side of the equation, 2x + 3, as Y1. Enter the expression on the right side of the equation, x + 5, as Y2. +3 5+ 2Y= ENTER Technology 4.4 X,T, ,n 1 of 3 For Figure 4.4a,

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Solving Equations Graphically Solve 2x + 3 = x + 5 graphically. Figure 4.4b Graph the equations. (In this case, we will use the standard window.) TRACE ENTER CALC ZOOM 2nd5 6 Find the intersection of the graphs. First trace the graph. Use the arrow keys to find the intersection. If the intersection cannot be found by tracing, use Intersect, option 5, under the CALC menu. Technology 4.4 2 of 3 For Figure 4.4b, Y1 = 2x + 3 Y2 = x + 5 (-10,10,-10,10)

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Solving Equations Graphically Solve 2x + 3 = x + 5 graphically. Figure 4.4c The solution is the x-value of the intersection point and is stored in x. The y-coordinate of the point of intersection is the value obtained for both the left side (Y1) and the right side (Y2) and is also stored. We can use this feature to check whether Y1 equals Y2. Quit the graph screen and enter x. VARSENTER VARS ENTERQUIT 2111 ► 2nd Enter Y1 and Y2. ► Since x = 2 when 7 = 7 (or Y1 = Y2), the solution of 2x + 3 = x + 5 is 2. For Figure 4.4c, Technology 4.4 X,T, ,n 3 of 3

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Section 1.2 Linear Equations and Rational Equations

Section 1.2 Linear Equations and Rational Equations

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