Explanation Given: The measure of one angle is 10 ° less than the measure of three times its complement 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. (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: Let one angle and its complement be x and y respectively. The statement “Sum of one angle and its complement is 90 ° ” can be translated as, x + y = 90 ° (1) The statement “The measure of one angle is 10 ° less than the measure of three times its complement” can be translated as, x − 3 y = − 10 ° (2) Step 1: The given equations are already in standard form. ( 1 ) x + ( 1 ) y = ( 90 ° ) ( 1 ) x − ( 3 ) y = ( − 10 ° ) Step 2: The coefficient of x in equation (1) is 1 and that in equation (2) x is 1 . So, x is a better choice of variable to be eliminated. Step 3: Multiply by 1 in equation (1) and by 1 in equation (2) and then subtract. x + y = 90 ° x − 3 y = − 10 ° _ 4 y = 100 ° This gives the equation 4 y = 100 °

3rd Edition

ISBN: 9780321880116

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

Publisher: PEARSON

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Chapter 4.4, Problem 28E

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The measure of the two angles.

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Elementary & Intermediate Algebra

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The measure of the two angles.

Solution Summary: The author explains the procedure of solving linear equations by elimination.

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