Math / Algebra

QuestionConsider the system of linear equations shown below: $\begin{array}{c} 2 x+9=-4 y \\ -x-y=2 \end{array}$
Create the coefficient matrix, $D$

Studdy Solution

STEP 1

1. The system of linear equations is given in the standard form $ax + by = c$ .
2. We need to extract coefficients of $x$ and $y$ from each equation to form the coefficient matrix.

STEP 2

1. Rearrange each equation to the standard form $ax + by = c$ .
2. Extract coefficients of $x$ and $y$ to form the coefficient matrix $D$ .

STEP 3

Rearrange the first equation $2x + 9 = -4y$ to the standard form:
$2x + 4y = -9$
This is done by adding $4y$ to both sides and subtracting 9 from both sides.

STEP 4

The second equation is already in the standard form:
$-x - y = 2$
No rearrangement is needed.

STEP 5

Extract the coefficients of $x$ and $y$ from both equations:
From the first equation $2x + 4y = -9$ , the coefficients are $2$ and $4$ .
From the second equation $-x - y = 2$ , the coefficients are $-1$ and $-1$ .

STEP 6

Form the coefficient matrix $D$ using the extracted coefficients:
$D = \begin{bmatrix} 2 & 4 \\ -1 & -1 \end{bmatrix}$
This matrix represents the coefficients of $x$ and $y$ in the system of equations.

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QuestionConsider the system of linear equations shown below: $\begin{array}{c} 2 x+9=-4 y \\ -x-y=2 \end{array}$
Create the coefficient matrix, $D$

Studdy Solution

STEP 1

1. The system of linear equations is given in the standard form $ax + by = c$ .
2. We need to extract coefficients of $x$ and $y$ from each equation to form the coefficient matrix.

STEP 2

1. Rearrange each equation to the standard form $ax + by = c$ .
2. Extract coefficients of $x$ and $y$ to form the coefficient matrix $D$ .

STEP 3

Rearrange the first equation $2x + 9 = -4y$ to the standard form:
$2x + 4y = -9$
This is done by adding $4y$ to both sides and subtracting 9 from both sides.

STEP 4

The second equation is already in the standard form:
$-x - y = 2$
No rearrangement is needed.

STEP 5

Extract the coefficients of $x$ and $y$ from both equations:
From the first equation $2x + 4y = -9$ , the coefficients are $2$ and $4$ .
From the second equation $-x - y = 2$ , the coefficients are $-1$ and $-1$ .

STEP 6

Form the coefficient matrix $D$ using the extracted coefficients:
$D = \begin{bmatrix} 2 & 4 \\ -1 & -1 \end{bmatrix}$
This matrix represents the coefficients of $x$ and $y$ in the system of equations.

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QuestionConsider the system of linear equations shown below: 2x+9=−4y−x−y=2\begin{array}{c} 2 x+9=-4 y \\ -x-y=2 \end{array}2x+9=−4y−x−y=2​Create the coefficient matrix, DDD

Studdy Solution

STEP 1

1. The system of linear equations is given in the standard form ax+by=c ax + by = c ax+by=c.2. We need to extract coefficients of x x x and y y y from each equation to form the coefficient matrix.

STEP 2

1. Rearrange each equation to the standard form ax+by=c ax + by = c ax+by=c.2. Extract coefficients of x x x and y y y to form the coefficient matrix D D D.

STEP 3

Rearrange the first equation 2x+9=−4y 2x + 9 = -4y 2x+9=−4y to the standard form:2x+4y=−9 2x + 4y = -9 2x+4y=−9This is done by adding 4y 4y 4y to both sides and subtracting 9 from both sides.

STEP 4

The second equation is already in the standard form:−x−y=2 -x - y = 2 −x−y=2No rearrangement is needed.

STEP 5

Extract the coefficients of x x x and y y y from both equations:From the first equation 2x+4y=−9 2x + 4y = -9 2x+4y=−9, the coefficients are 2 2 2 and 4 4 4.From the second equation −x−y=2 -x - y = 2 −x−y=2, the coefficients are −1 -1 −1 and −1 -1 −1.

STEP 6

Form the coefficient matrix D D D using the extracted coefficients:D=[24−1−1] D = \begin{bmatrix} 2 & 4 \\ -1 & -1 \end{bmatrix} D=[2−1​4−1​]This matrix represents the coefficients of x x x and y y y in the system of equations.

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QuestionConsider the system of linear equations shown below: $\begin{array}{c} 2 x+9=-4 y \\ -x-y=2 \end{array}$
Create the coefficient matrix, $D$

1. The system of linear equations is given in the standard form $ax + by = c$ .
2. We need to extract coefficients of $x$ and $y$ from each equation to form the coefficient matrix.

1. Rearrange each equation to the standard form $ax + by = c$ .
2. Extract coefficients of $x$ and $y$ to form the coefficient matrix $D$ .

Rearrange the first equation $2x + 9 = -4y$ to the standard form:
$2x + 4y = -9$
This is done by adding $4y$ to both sides and subtracting 9 from both sides.

The second equation is already in the standard form:
$-x - y = 2$
No rearrangement is needed.

Extract the coefficients of $x$ and $y$ from both equations:
From the first equation $2x + 4y = -9$ , the coefficients are $2$ and $4$ .
From the second equation $-x - y = 2$ , the coefficients are $-1$ and $-1$ .

Form the coefficient matrix $D$ using the extracted coefficients:
$D = \begin{bmatrix} 2 & 4 \\ -1 & -1 \end{bmatrix}$
This matrix represents the coefficients of $x$ and $y$ in the system of equations.