Question 10 • Advanced Algebra: Concepts and Connections
In the matrix equation, what are the values of x and y ? 1 half the 2 by 2 matrix, row 1, column 1, 4 column 2, 8 row 2, column 1, x plus 3 column 2, negative 4 minus 3 the 2 by 2 matrix, row 1, column 1, 1 column 2, y plus 1 row 2, column 1, negative 1 column 2, negative 2 is equal to the 2 by 2 matrix, row 1, column 1, negative 1 column 2, negative 5 row 2, column 1, 7 column 2, 4
Answer
A
x is equal to 3 , y is equal to 8
B
x is equal to 5 , y is equal to negative 4
C
x is equal to negative 1 , y is equal to 2
D
x is equal to 5 , y is equal to 2
Explanation
Compare the entries in the same positions on both sides. In the top-right position, ½(8) − 3(y + 1) = −5, so 4 − 3y − 3 = −5, giving y = 2. In the bottom-left position, ½(x + 3) − 3(−1) = 7, so (x + 3)/2 + 3 = 7, giving x = 5. The correct choice is D: x = 5 and y = 2.
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