Answer:
Option C is correct
value of the x-determinant for the system is, -2
Step-by-step 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
