Question

If the following system of equations was written as a matrix equation in the form AX = C, and matrix A was expressed in the form: A= {A C} {B D}, find the value of a-b +c+d. 2x+8y=7 4x-2y=9 Please help, i dont know which number would be which letters

Answer 1

Matrix A ={ 2 8}{4 -2}, so a-b+c+d = 2-4+8+(-2) = 4

Answer 2

Answer: a-b+c+d =4

Explanation:

The given system of equation is

`2x+8y=7\\4x-2y=9`

from this we have the following matrices

`A_1 =\begin{bmatrix}\\2 &8 \\ \\4&2 \\\end{bmatrix}\ ,X=\begin{bmatrix}\\x\\ \\y\\\end{bmatrix}\text{and}\ C=\begin{bmatrix}\\7\\ \\9\\\end{bmatrix}`

the given matrix A =
`\begin{bmatrix}\\a &c \\ \\b &d \\\end{bmatrix}`

On comparing Matrix
`A_1` with Matrix A

`\begin{bmatrix}\\a &c \\ \\b &d \\\end{bmatrix}=\begin{bmatrix}\\2&8 \\ \\4 &-2 \\\end{bmatrix}`

we have the following values

a=2 ,b=4,c=8,d=-2

Thus a-b+c+d =2-4+8+(-2)=4