Explanation Procedure used: “Solving system of linear equations by elimination” (1) If the equations are not in the standard form, then they are converted accordingly into a standard form which is as follows: a x + b y = c Where x and y are variables and a , b and c are appropriate integer constants. (2) The variable to be eliminated is recognized from the given equations in the system. (3) After obtaining the LCM (lowest common multiple) of coefficients of the variable to be eliminated, the equations are multiplied with appropriate multipliers so that the coefficients in each equation become additive inverses and adding the new equations will result in a fresh equation with the decided variable to been eliminated. (4) The equation in step (3) is solved obtaining value of remaining variable. (5) The value of variable in step (4) is substituted to the equation in any of the given system equations. (6) Solving the equation obtained in step (5) gives the value of variable eliminated in step (3). (7) The correctness of solution is asserted by substituting back the values in given equations of the system. Calculation: Name the given equations as, 2 x + 3 y = 2 (1) 5 x + 7 y = 0 (2) Step 1: Both equations (1) and (2) are already in standard form, no need to arrange in standard form. Step 2: Arbitrarily select variable x for elimination, in the given linear system of equations. Step 3: The coefficients of x in the equations are 2 and 5 , whose LCM is 10 . Thus, in order to make the coefficients of x to additive inverses, equation (1) is to be multiplied by 5 and equation (2) is to be multiplied by − 2 . Since the coefficients of x became additive inverses, the equations can be added. 10 x + 15 y = 10 − 10 x − 14 y = 0 _ y = 10 Step 4: From step 3, the value of y = 10 . Step 5: Substitute y = 10 in equation (1). 2 x + 3 ( 10 ) = 2 2 x = 2 − 30 2 x = − 28 Step 6: Solve the above equation for x

4th Edition

ISBN: 9780134556079

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

Publisher: Pearson,

See similar textbooks

Videos

Question

Chapter 4.3, Problem 34E

To determine

To solve: The system of linear equations 2x+3y=2 and 5x+7y=0 by elimination method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.3, Problem 33E

Chapter 4.3, Problem 35E

Students have asked these similar questions

In Problems 19–56, solve each system of equations. If the system has no solution, say that it is inconsistent. For Problems 19–30, graphthe lines of the system

Help me answer in full details

In Problems 1–6, find the real solutions of each equation.

Chapter 4 Solutions

Elementary & Intermediate Algebra

Ch. 4.1 - A _____ is a grouping of two or more linear...Ch. 4.1 - A _____ of a system of equations consists of...Ch. 4.1 - Prob. 3E Ch. 4.1 - In Problems 3 and 4, determine whether each...Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - In Problem 8, solve the system by graphing. 8....Ch. 4.1 - Prob. 9E Ch. 4.1 - If a system of linear equations in two variables...

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The system of linear equations 2 x + 3 y = 2 and 5 x + 7 y = 0 by elimination method.

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

Videos

To solve: The system of linear equations 2x+3y=2 and 5x+7y=0 by elimination method.

Want to see the full answer?

Chapter 4 Solutions