Question 15 • Advanced Algebra: Concepts and Connections
Which system of linear equations can be solved using the equation the 2 by 1 column matrix x y is equal to the 2 by 2 matrix, row 1, column 1, 1 fourth column 2, 3 fourths row 2, column 1, 1 column 2, 2 the 2 by 1 column matrix row 1 28 row 2 negative 12 ?
Answer
A
1 fourth x plus y is equal to 28 3 fourths x plus 2 y is equal to negative 12
B
negative 8 x plus 3 y is equal to 28 4 x minus y is equal to negative 12
C
1 fourth x plus 3 fourths y is equal to 28 x plus 2 y is equal to negative 12
D
negative 8 x plus 4 y is equal to 28 3 x minus y is equal to negative 12
Explanation
In a matrix equation, each row of the 2 by 2 matrix gives one equation. The first row, (1/4, 3/4), gives (1/4)x + (3/4)y = 28; the second row, (1, 2), gives x + 2y = -12. So the matching system is choice C.
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