Math  /  Algebra

QuestionConsider the system of linear equations shown below: 2x+9=4yxy=2\begin{array}{l} 2 x+9=-4 y \\ -x-y=2 \end{array} create the matrix, DxD_{x}

Studdy Solution

STEP 1

1. We are working with a system of linear equations.
2. The matrix Dx D_x refers to the determinant of the coefficient matrix with the first column replaced by the constants from the right-hand side of the equations.
3. We will use Cramer's Rule to find the matrix Dx D_x .

STEP 2

1. Rewrite the system of equations in standard form.
2. Identify the coefficient matrix and the constant matrix.
3. Form the matrix Dx D_x by replacing the first column of the coefficient matrix with the constant matrix.

STEP 3

Rewrite the system of equations in standard form:
The given system is: 2x+4y=9xy=2\begin{array}{l} 2x + 4y = -9 \\ -x - y = 2 \end{array}
Rewriting it in standard form: 2x+4y=9xy=2\begin{array}{l} 2x + 4y = -9 \\ -x - y = 2 \end{array}

STEP 4

Identify the coefficient matrix and the constant matrix:
The coefficient matrix A A is: A=[2411]A = \begin{bmatrix} 2 & 4 \\ -1 & -1 \end{bmatrix}
The constant matrix (right-hand side) is: B=[92]B = \begin{bmatrix} -9 \\ 2 \end{bmatrix}

STEP 5

Form the matrix Dx D_x by replacing the first column of the coefficient matrix with the constant matrix:
The matrix Dx D_x is: Dx=[9421]D_x = \begin{bmatrix} -9 & 4 \\ 2 & -1 \end{bmatrix}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord