Explanation Procedure used: Solving system of linear equations by elimination: Step 1 : Write both equations of the system in the standard form, A x + B y = C . If necessary, multiply both sides of one equation or both equations by a no-zero constant so that the coefficients of one of the variables are now additive inverses. Step 2 : Add equations (1) and (2) to eliminate the variable whose coefficients are now additive inverses. Solve the resulting equation for the unknown. Here, sometimes the variables get eliminated, and either a true statement or a false statement result. If a true statement is obtained, the system has infinite solutions and is consistent and the equations are dependent, and if a false statement is obtained, then no solution exists and the system is inconsistent and the equations are independent. Step 3 : Substitute the value of the variable found in step 2 into one of the original equations to find the remaining variable. Step 4 : Check the answer by substituting the ordered pair in both of the original equations. Calculation: The given system of equations is, { 2 x − 3 y = − 9 ⋯ ( 1 ) − x + 5 y = 8 ⋯ ( 2 ) Multiply equation (2) by 2 in order to make the coefficients of the variable x additive inverses and then add the resulting equation with equation (1) to eliminate the variable x . 2 x − 3 y = − 9 − 2 x + 10 y = 16 _ 7 y = 7 Solve the equation 7 y = 7 for y . 7 y = 7 y = 7 7 y = 1 Substitute y = 1 in equation (2)

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ISBN: 9780134556079

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

Publisher: Pearson,

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Chapter 12.5, Problem 47E

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To solve: The system {2x−3y=−9−x+5y=8 using either substitution or elimination.

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Chapter 12.5, Problem 46E

Chapter 12.5, Problem 48E

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The system { 2 x − 3 y = − 9 − x + 5 y = 8 using either substitution or elimination.

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

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To solve: The system {2x−3y=−9−x+5y=8 using either substitution or elimination.

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Chapter 12 Solutions