EXAMPLE 2 In-Class Example 2 Solve the system by the substitution method. x 3y 5 2x 5y 23 Answer: (4, 3) Notice that, in the first equation in Example 2, the coefficient of x is 1 so that it is easiest to begin by solving for this variable. Let’s summarize the steps we use to solve a system by the substitution method. Procedure Solving a System by the Substitution Method Step 1: Solve one of the equations for one of the variables. If possible, solve for a variable that has a coeffi cient of 1 or 1. Step 2: Substitute the expression found in Step 1 into the other equation. The equation you obtain should contain only one variable. Step 3: Solve the equation you obtained in Step 2. Step 4: Substitute the value found in Step 3 into either of the equations to obtain the value of the other variable. Step 5: Check the values in each of the original equations, and write the solution as an ordered pair. Solve the system by the substitution method. x 2y 7 (1) 2x 3y 21 (2) Solution We will follow the steps listed in the Procedure box. Step 1: For which variable should we solve? The x in the fi rst equation is the only variable with a coeffi cient of 1 or 1. Therefore, we will solve the fi rst equation for x. x 2y 7 First equation (1) x 2y 7 Add 2y. Step 2: Substitute 2y 7 for the x in equation (2). 2x 3y 21 Second equation (2) 2(2y 7) 3y 21 Substitute. Step 3: Solve this new equation for y. 2(2y 7) 3y 21 4y 14 3y 21 Distribute. 7y 14 21 Combine like terms. 7y 35 Subtract 14 from each side. y 5 Step 4: To determine the value of x, we can substitute 5 for y in either equation. We will use equation (1). x 2y 7 Equation (1) x 2(5) 7 Substitute. x 10 7 x 3 Step 5: The check is left to the reader. The solution of the system is (3, 5). 256 CHAPTER 4 Linear Equations and Inequalities in Two Variables www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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