Which equation can be used to solve for the y -value of the solution in the given system of linear equations? negative 6 x plus 4 y is equal to negative 62 negative 3 x minus 5 y is equal to negative 17

Answer

A

the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 62 column 2, 4 row 2, column 1, negative 17 column 2, negative 5 and denominator the 2 by 2 matrix, row 1, column 1, negative 6 column 2, 4 row 2, column 1, negative 3 column 2, negative 5 is equal to negative 2

B

the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 6 column 2, negative 62 row 2, column 1, negative 3 column 2, negative 17 and denominator the 2 by 2 matrix, row 1, column 1, negative 6 column 2, 4 row 2, column 1, negative 3 column 2, negative 5 is equal to negative 2

C

the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 6 column 2, negative 62 row 2, column 1, negative 3 column 2, negative 17 and denominator the 2 by 2 matrix, row 1, column 1, negative 6 column 2, 4 row 2, column 1, negative 3 column 2, negative 5 is equal to 9

D

the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 62 column 2, 4 row 2, column 1, negative 17 column 2, negative 5 and denominator the 2 by 2 matrix, row 1, column 1, negative 6 column 2, 4 row 2, column 1, negative 3 column 2, negative 5 is equal to 9

Explanation

To find the y-value using Cramer’s rule, replace the y-column of the coefficient matrix with the constants: the numerator is the determinant of [[-6, -62], [-3, -17]]. The denominator is the determinant of the original coefficient matrix, [[-6, 4], [-3, -5]]. Their ratio is (102 − 186) ÷ (30 + 12) = −84 ÷ 42 = −2, so the equation in choice A gives the y-value.

AI-written and checked against the verified answer.

Practice Test

Which equation can be used to solve for the y -value of the solution in the given system of linear equations? negative 6 x plus 4 y is equal to negative 62 negative 3 x minus 5 y is equal to negative 17

Explanation

More from this Course