Question 9 • Advanced Algebra: Concepts and Connections
Which system of linear equations can be solved using the given information? start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, 20 column 2, negative 3 row 2, column 1, negative 192 column 2, 8 start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, 2 column 2, 20 row 2, column 1, 12 column 2, negative 192
Answer
A
negative 3 x plus 8 y is equal to 20 2 x plus 12 y is equal to negative 192
B
20 x minus 3 y is equal to 2 negative 192 x plus 8 y is equal to 12
C
negative 3 x plus 2 y is equal to 20 8 x plus 12 y is equal to negative 192
D
2 x minus 3 y is equal to 20 12 x plus 8 y is equal to negative 192
Explanation
In Cramer’s rule, the matrix for Aₓ replaces the x-coefficient column with the constants. From Aₓ, the constants are 20 and −192, and the y-coefficients are −3 and 8. The matrix for Aᵧ shows the x-coefficients are 2 and 12. So the system is 2x − 3y = 20 and 12x + 8y = −192, which is choice A.
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