Explanation Given Information: The provided system of equations are, x = y − 1 3 y = 2 x + 9 Formula Used: The Cramer’s rule to solve system of the equation is as follows: The standard form of the system of equation in two variables x and y is given by, a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2 The determinant D is obtained by using coefficient of the variables in the form of | a 1 b 1 a 2 b 2 | , that is D = | a 1 b 1 a 2 b 2 | , The determinant D x is obtained by replacing a 1 , a 2 by c 1 , c 2 respectively in determinant D , that is D x = | c 1 b 1 c 2 b 2 | . And, similarly D y is obtained by replacing b 1 , b 2 by c 1 , c 2 respectively in determinant D , that is D y = | a 1 c 1 a 2 c 2 | Then, the variables x and y are computed as, x = D x D and y = D y D , provided D ≠ 0 Where, the value of a determinant is calculated as follows: A = | a c b d | = a d − b c Calculation: Consider the provided system of equations, x = y − 1 3 y = 2 x + 9 Write the equations in standard form, that is, x − y = − 1 2 x − 3 y = − 9 Compare the system of equations x − y = − 1 , 2 x − 3 y = − 9 with standard form of equations a 1 x + b 1 y = c 1 , a 2 x + b 2 y = c 2 , this gives, a 1 = 1 , a 2 = 2 , b 1 = − 1 , b 2 = − 3 , c 1 = − 1 and c 2 = − 9 , Now, calculate the values of D , D x and D y with t

Intermediate Algebra For College Students (10th Edition)

10th Edition

ISBN: 9780134758992

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

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Chapter 4.5, Problem 24ES

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To calculate: The solution of the system of equations x=y−1,3y=2x+9, by using determinants.

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Chapter 4.5, Problem 23ES

Chapter 4.5, Problem 25ES

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The solution of the system of equations x = y − 1 , 3 y = 2 x + 9 , by using determinants.

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To calculate: The solution of the system of equations x=y−1,3y=2x+9, by using determinants.

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Chapter 4 Solutions