Practice Test

Question 4 • Advanced Algebra: Concepts and Connections

Which determinants can be used to solve for x and y in the given system of linear equations? 4 x plus 16 y is equal to negative 68 12 x plus 3 y is equal to 21

Answer

absolute value of cap A is equal to the 2 by 2 matrix row 1, 4 16 row 2, 12 3 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, 4 column 2, 16 row 2, column 1, negative 68 column 2, 21 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 68 column 2, 21 row 2, column 1, 12 column 2, 3

absolute value of cap A is equal to the 2 by 2 matrix row 1, 4 16 row 2, 12 3 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, 4 column 2, negative 68 row 2, column 1, 12 column 2, 21 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 68 column 2, 16 row 2, column 1, 21 column 2, 3

absolute value of cap A is equal to the 2 by 2 matrix row 1, 4 16 row 2, 12 3 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 68 column 2, 21 row 2, column 1, 12 column 2, 3 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, 4 column 2, 16 row 2, column 1, negative 68 column 2, 21

absolute value of cap A is equal to the 2 by 2 matrix row 1, 4 16 row 2, 12 3 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, negative 68 column 2, 16 row 2, column 1, 21 column 2, 3 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, 4 column 2, negative 68 row 2, column 1, 12 column 2, 21

Explanation

For Cramer’s rule, the coefficient determinant is |A| = [[4, 16], [12, 3]]. To form |Aₓ|, replace the first (x) column with the constants −68 and 21, giving [[−68, 16], [21, 3]]. To form |Aᵧ|, replace the second (y) column instead, giving [[4, −68], [12, 21]]. These are the determinants shown in choice A.

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