Using Cramer’s Rule, what is the value of x in the solution to the given system of equations? negative x minus 3 y is equal to negative 3 negative 2 x minus 5 y is equal to negative 8
Answer
A
the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 1 column 2, negative 3 row 2, column 1, negative 2 column 2, negative 8 and denominator negative 1 is equal to negative 2
B
the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 3 column 2, negative 3 row 2, column 1, negative 8 column 2, negative 5 and denominator negative 1 is equal to 9
C
the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 3 column 2, negative 3 row 2, column 1, negative 8 column 2, negative 5 and denominator negative 1 is equal to negative 2
D
the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 1 column 2, negative 3 row 2, column 1, negative 2 column 2, negative 8 and denominator negative 1 is equal to 9
Explanation
For Cramer’s Rule, replace the x-column of the coefficient matrix with the constants −3 and −8. The resulting determinant is (−3)(−5) − (−3)(−8) = 15 − 24 = −9. The coefficient determinant is (−1)(−5) − (−3)(−2) = 5 − 6 = −1, so x = (−9)/(−1) = 9. Choice B gives this determinant calculation and value.
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