Question

X + y = 12

x - y = 10

What is the value of the x-determinant for the system shown?

a)-22
b)-12
c)-2

Answer 1

Option C is correct

value of the x-determinant for the system is, -2

Explanation:

Given the system of equation:

x + y =12

x -y =10

Represents the system of equations in matrix format:

`\begin{bmatrix} 1 & 1\\ 1 & -1 \end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}12\\ 10\end{bmatrix}`

Now, to find the determinant of a matrix.

Formula for the determinant of matrix:

`\begin{bmatrix}a & b\\ c & d\end{bmatrix} = ad-bc`

then;

The value of the x-determinant:

`\begin{bmatrix}1 & 1\\ 1 & -1\end{bmatrix}`

Using determinant(D) formula:

`D= (1)(-1)-(1)(1) = -1 -1 = -2`

Therefore, the value of the x-determinant for the system is, -2