Explanation Procedure used: “ Solving linear systems by Substitution: (1) Solve either of the equations for one variable in terms of the other. (If one of the equations is already in this form, you can skip this step.) (2) Substitute the expression found in step 1 into the other equation. (3) Solve the equation containing one variable. (4) Sometimes variables have been eliminated, and either true statement or false statement results then that means system has infinite solution for true statement or no solution exist for false statement. (5) If neither the case follow the next steps otherwise not. (6) Back-substitute the value found in step 3 into one of the original equations. Simplify and find the value of the remaining variable. (7) Check the proposed solution in both of the system’s given equations”. Calculation: Consider the given equations. y = 3 x − 2 ( 1 ) 2 x − 3 y = − 8 ( 2 ) Step 1: Since the equation (1) is already in the form of y in terms of x , no need to isolate the variable. Step 2: Substitute y = 3 x − 2 in the equation (2), 2 x − 3 y = − 8 2 x − 3 ( 3 x − 2 ) = − 8 Here, the variable y eliminated. Step 3: Solve the equation obtained in step 2. 2 x − 3 ( 3 x − 2 ) = − 8 2 x − 9 x + 6 = − 8 ( Combine like terms ) − 7 x = − 8 − 6 x = 2 Step 4: Now, substitute x = 2 in one of the given equation and obtain the value of y

4th Edition

ISBN: 9780134556079

Author: Sullivan, Michael, III, Struve, Katherine R., Mazzarella, Janet.

Publisher: Pearson,

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Chapter 4.2, Problem 2E

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To solve: The system of linear equations y=3x−2 and 2x−3y=−8 by substitution.

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Chapter 4.2, Problem 1E

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The system of linear equations y = 3 x − 2 and 2 x − 3 y = − 8 by substitution.

Solution Summary: The author explains how to solve the system of linear equations by substitution.

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To solve: The system of linear equations y=3x−2 and 2x−3y=−8 by substitution.

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