14
QuizMultiple Choice

N/A — Exam

Question 14 • Algebraic Reasoning

Consider the system of linear equations and the matrix equations. negative x plus 3 y is equal to 2 4 x minus 2 y is equal to 22 the 2 by 2 matrix, row 1, column 1, negative 1 column 2, 3 row 2, column 1, 4 column 2, negative 2 the 2 by 1 column matrix x y is equal to the 2 by 1 column matrix 2 22 What is the value of x in the equation?

Answer
A
64
B
7
C
3
D
negative 36

Explanation

From the second equation, 4x − 2y = 22, divide both sides by 2 to get 2x − y = 11, so y = 2x − 11. Substitute this into the first equation: −x + 3(2x − 11) = 2. Simplifying gives 5x − 33 = 2, so 5x = 35 and x = 7. The correct choice is B, 7.

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