Question 8 • Advanced Algebra: Concepts and Connections
Based on the given information, what are the values of x and y of the solution to the system of equations used to create the information? absolute value of cap A is equal to the 2 by 2 matrix, row 1, column 1, 4 column 2, negative 6 row 2, column 1, 8 column 2, negative 2 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, 38 column 2, negative 6 row 2, column 1, 26 column 2, negative 2 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix row 1, 4 38 row 2, 8 26
Answer
A
x is equal to 2 comma y is equal to negative 5
B
x is equal to negative 5 comma y is equal to 2
C
x is equal to 0 point 5 comma y is equal to negative 0 point 2
D
x is equal to negative 0 point 2 comma y is equal to 0 point 5
Explanation
Using Cramer's rule, x = det(Aₓ) / det(A) and y = det(Aᵧ) / det(A). The determinant of A is 4(−2) − (−6)(8) = 40, and the determinant of Aₓ is 38(−2) − (−6)(26) = 80, so x = 80/40 = 2. The determinant of Aᵧ is 4(26) − 38(8) = −200, so y = −200/40 = −5. The correct choice is C: x = 2 and y = −5.
AI-written and checked against the verified answer.