Provide an appropriate response.
-For a certain system of two linear equations, the solution set is $\{ - 9,5 \}$, and $D = 9$. Find the values of $D _ { x }$ and $D _ { y }$.
A) $\mathrm { D } _ { \mathrm { X } } = - 1 ; \mathrm { D } _ { \mathrm { y } } = \frac { 5 } { 9 }$
B) $\mathrm { D } _ { \mathrm { x } } = 45 ; \mathrm { D } _ { \mathrm { y } } = - 81$
C) $\mathrm { D } _ { \mathrm { x } } = - 81 ; \mathrm { D } _ { \mathrm { y } } = 45$
D) $D _ { \mathrm { X } } = - 9 ; \mathrm { D } _ { \mathrm { y } } = 5$

Question

Quizplus · Accepted Answer

Given the solution set $\{ - 9,5 \}$ and $D = 9$, $D_x$ and $D_y$ can be found using Cramer's Rule, which involves the determinants of matrices. $D_x$ is the determinant of the matrix formed by replacing the x-column of the coefficient matrix with the solution column, and $D_y$ is found similarly by replacing the y-column. Since the solution set is given as $\{ - 9,5 \}$, and knowing $D$, we can calculate $D_x = xD = -9 \times 9 = -81$ and $D_y = yD = 5 \times 9 = 45$, which matches option C.

Provide an Appropriate Response {−9,5}\{ - 9,5 \}{−9,5} , And D=9D = 9D=9

Provide an Appropriate Response $\{ - 9,5 \}$ , And $D = 9$