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. (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 and Solving the equation. (6) The correctness of solution is asserted by substituting back the values in given equations of the system. Calculation: Let one angle and its supplement as x and y respectively. So, according to question, Sum of one angle and its supplement is 180 ° . It can be represented as: x + y = 180 ° (1) Second statement is that the measure of one angle is 30 ° less than three times the measure of its supplement. It can be represented as: x − 3 y = − 30 ° (2) Step 1: Since the given equations are already in standard form, nothing has to be done. ( 1 ) x + ( 1 ) y = ( 180 ° ) ( 1 ) x − ( 3 ) y = ( − 30 ° ) Step 2: The coefficient of x in (1) equation is 1 and that in (2) equation x is 1 . So, x is a better choice of the variable to be eliminated. Step 3: Multiply by 1 in (1) equation and by 1 in equation (2) and then subtract both the equations: x + 1 y = 180 ° x − 3 y = − 30 ° _ 4 y = 210 ° Step 4: The equation obtained in Step (3) is solved: 4 y = 210 ° y = 210 4 y = 52.5 ° Thus, the value of y is 52.5 ° . Step-5: Now, substitute the value of y = 52.5 ° in the equation (1) as follows. x + y = 180 ° x + 52

3rd Edition

ISBN: 9780321880116

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

Publisher: PEARSON

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Chapter 4, Problem 16T

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To find: The measure of two angles.

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Chapter 4, Problem 15T

Chapter 4, Problem 17T

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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...

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The measure of two angles.

Solution Summary: The author explains the procedure of solving linear equations by elimination. The measure of one angle and its supplement is 180°.

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To find: The measure of two angles.

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