Explanation Procedure used: “ Solving linear systems by Substitution: Step 1: Solve one of the equations for one of the unknowns. Step 2: Substitute the expression found in Step 1 into the other equation. The result will be a single linear equation in one unknown. Step 3: Solve the linear equation in one unknown found in Step 2. Step 4: Substitute the value of the variable found in step 3 into one of the original equations to find the value of the other variable. Write the solution as an ordered pair, if possible. Step 5: Check you answer by substituting the ordered pair into both of the original equations”. Calculation: Consider the given equations. 2 x − 3 y = − 10 (1) − 3 x + y = 1 (2) Step 1: Isolate y in term of x in the equation (2). − 3 x + y = 1 y = 1 + 3 x Step 2: Substitute 1 + 3 x for y in the equation (1), 2 x − 3 y = − 10 2 x − 3 ( 1 + 3 x ) = − 10 Here, the variable y is eliminated. Step 3: Solve the equation obtained in step 2. 2 x − 3 ( 1 + 3 x ) = − 10 2 x − 3 − 9 x = − 10 ( Combine like terms ) − 7 x = − 7 x = 1 Step 4: Now, substitute 1 for x in one of the given equation and obtain the value of y . Replace variable x with 1 in equation (2). − 3 x + y = 1 − 3 ( 1 ) + y = 1 y = 4 Thus, the required solution is ( 1 , 4 ) . Step 5: Check whether the obtained solution ( 1 , 4 ) satisfies the given equations or not. Replace variable x with 1 and variable y with 4 , in the equation (1)

4th Edition

ISBN: 9780134556079

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

Publisher: Pearson,

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Chapter 4.3, Problem 52E

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To solve: The system of linear equations 2x−3y=−10 and −3x+y=1 by substitution method.

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Chapter 4.3, Problem 51E

Chapter 4.3, Problem 53E

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Chapter 4 Solutions

Elementary & Intermediate Algebra

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The system of linear equations 2 x − 3 y = − 10 and − 3 x + y = 1 by substitution method.

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To solve: The system of linear equations 2x−3y=−10 and −3x+y=1 by substitution method.

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