Solve the system using the elimination method. x y 11 (1) x y 5 (2) Solution The left side of each equation is equal to the right side of each equation. Therefore, if we add the left sides together and add the right sides together, we can set them equal. We will add these equations vertically. The y-terms are eliminated, enabling us to solve for x. x y 11 (1) x y 5 (2) 2x 0y 6 Add equations (1) and (2). 2x 6 Simplify. x 3 Divide by 2. Now we substitute x 3 into either equation to fi nd the value of y. Here, we will use equation (1). x y 11 Equation (1) 3 y 11 Substitute 3 for x. y 8 Subtract 3. Check x 3 and y 8 in both equations. x y 11 x y 5 3 8 11 Substitute. 3 8 5 Substitute. 11 11 True 5 5 True The solution of the system is (3, 8). Are you writing out the steps in the example as you are reading it? YOU TRY 1 Solve the system using the elimination method. 3x y 10 x y 6 In Example 1, simply adding the equations eliminated a variable. But what can we do if we cannot eliminate a variable just by adding the equations together? EXAMPLE 1 In-Class Example 1 Solve the system using the elimination method. x 4y 1 x y 6 Answer: (5, 1) EXAMPLE 2 In-Class Example 2 Solve the system using the elimination method. 3x y 4 2x 5y 20 Answer: (0, 4) Solve the system using the elimination method. 2x 5y 5 (1) x 4y 7 (2) Solution Just adding these equations will not eliminate a variable. The multiplication property of equality tells us that multiplying both sides of an equation by the same quantity results in an equivalent equation. If we multiply equation (2) by 2, the coeffi cient of x will be 2. 2(x 4y) 2(7) Multiply equation (2) by 2. 2x 8y 14 New, equivalent equation Original System Rewrite the System 2x 5y 5 2x 5y 5 x 4y 7 2x 8y 14 Notice that we multiply the second equation by 2 so that the coefficients of x are opposites. This way, when you add the two equations together, the x’s are eliminated. www.mhhe.com/messersmith SECTION 4.3 Solving Systems by the Elimination Method 263
messersmith_power_introductory_algebra_1e_ch4_7_10
To see the actual publication please follow the link above