Questions: Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write integers or simplified fractions. -10x - 3y = -9 -8x - 6y = -5 Part 1 of 2 Evaluate the determinants D, Dx, and Dy. D = □ Dx = □ Dy = □

$Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write integers or simplified fractions. -10x - 3y = -9 -8x - 6y = -5 Part 1 of 2 Evaluate the determinants D, Dx, and Dy. D = □ Dx = □ Dy = □$

Transcript text: Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write a integers or simplified fractions. \[ \begin{array}{r} -10 x-3 y=-9 \\ -8 x-6 y=-5 \end{array} \] Part: $0 / 2$ Part 1 of 2 Evaluate the determinants $D_{1} D_{x}$, and $D_{y}$. \[ D=\square \quad D_{x}=\square \quad D_{y}=\square \] $\square$ $\square$ $\square$ $\square$

Solution

Solution Steps

To solve the system using Cramer's rule, we first need to evaluate the determinant $ D $ of the coefficient matrix. If $ D \neq 0 $, Cramer's rule can be applied. We then calculate the determinants $ D_x $ and $ D_y $ by replacing the respective columns of the coefficient matrix with the constant terms. If $ D = 0 $, Cramer's rule cannot be applied, and we would need to use another method, such as substitution or elimination, to solve the system.

Step 1: Calculate the Determinant $ D $

The determinant $ D $ of the coefficient matrix is calculated as follows:

\[ D = 36.0 \]

Step 2: Calculate the Determinant $ D_x $

To find $ D_x $, we replace the first column of the coefficient matrix with the constants:

\[ D_x = 38.99999999999999 \approx 39.0 \]

Step 3: Calculate the Determinant $ D_y $

To find $ D_y $, we replace the second column of the coefficient matrix with the constants:

\[ D_y = -22.000000000000004 \approx -22.0 \]