Page 17

messersmith_power_introductory_algebra_1e_ch4_7_10

Read the explanations, follow the examples, take notes, and complete the You Trys. In Section 4.1, we learned to solve a system of equations by graphing. This method, however, is not always the best way to solve a system. If your graphs are not precise, you may read the solution incorrectly. And, if a solution consists of numbers that are not integers, like a2 3 , 1 4 b, it may not be possible to accurately identify the point of intersection of the graphs. 1 Solve a Linear System by Substitution Another way to solve a system of equations is to use the substitution method. When we use the substitution method, we solve one of the equations for one of the variables in terms of the other. Then we substitute that expression into the other equation. We can do this because solving a system means fi nding the ordered pair, or pairs, that satisfy both equations. The substitution method is especially good when one of the variables has a coeffi cient of 1 or 1. EXAMPLE 1 In-Class Example 1 Solve the system using substitution. y 4x 1 6x 5y 2 Answer: a 1 2 , 1b Solve the system using substitution. 2x 3y 1 y 2x 3 Solution The second equation, y 2x 3, is already solved for y; it tells us that y equals 2x 3. Therefore, we can substitute 2x 3 for y in the fi rst equation, then solve for x. 2x 3y 1 First equation 2x 3(2x 3) 1 Substitute. 2x 6x 9 1 Distribute. 8x 9 1 Combine like terms. 8x 8 Add 9 to each side. x 1 We have found that x 1, but we still need to fi nd y. Substitute x 1 into either equation, and solve for y. In this case, we will substitute x 1 into the second equation since it is already solved for y. y 2x 3 Second equation y 2(1) 3 Substitute. y 2 3 y 1 Check x 1, y 1 in both equations. 2x 3y 1 y 2x 3 2(1) 3(1) 1 Substitute. 1 2(1) 3 Substitute. 2 3 1 1 2 3 1 1 True 1 1 True We write the solution of the system as an ordered pair, (1, 1). Write out all of the steps in the example as you are reading it! Try graphing both of these equations. You will see that (1, 1) is the point of intersection. www.mhhe.com/messersmith SECTION 4.2 Solving Systems by the Substitution Method 255


messersmith_power_introductory_algebra_1e_ch4_7_10
To see the actual publication please follow the link above