Matrices — Test

Question 17 • Algebra II

Using Cramer’s Rule, what is the value of y for the solution to the given system of linear equations? 2 x minus y is equal to 3 5 x minus 2 y is equal to 8

Answer

the fraction with numerator the 2 by 2 matrix row 1, 2 3 row 2, 5 8 and denominator negative 1 is equal to negative 1

the fraction with numerator the 2 by 2 matrix, row 1, column 1, 3 column 2, negative 1 row 2, column 1, 8 column 2, negative 2 and denominator 1 is equal to 2

the fraction with numerator the 2 by 2 matrix row 1, 2 3 row 2, 5 8 and denominator 1 is equal to 1

the fraction with numerator the 2 by 2 matrix, row 1, column 1, 3 column 2, negative 1 row 2, column 1, 8 column 2, negative 2 and denominator negative 1 is equal to negative 2

Explanation

For Cramer’s Rule, the denominator is the determinant of the coefficient matrix: (2)(−2) − (−1)(5) = 1. To find y, replace the y-coefficient column with the constants, giving the matrix [[2, 3], [5, 8]]. Its determinant is (2)(8) − (3)(5) = 1, so y = 1 ÷ 1 = 1. Choice C gives this calculation and value.

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