Answer:
Given the system of equations, what is the value of the system determinant? x + y = 8
x - y = 10
C. -2
Given the system of equations, what is the value of the y-determinant?
3x + y - 10 = 0
4x - y - 4 = 0
A. -28
Step-by-step explanation:
The determinant of the system is the determinant of the matrix formed with the coefficients of the system, usually, this matrix is called A.
[tex]A=\left[\begin{array}{cc}1&1\\1&-1\end{array}\right][/tex]
In the 2x2 matrix, the determinant is calculated by obtaining the difference between the diagonally down product and the diagonally up product.
[tex]det(A)=\left|\begin{array}{cc}1&1\\1&-1\end{array}\right|=(1)(-1)-(1)(1)=-1-1=-2[/tex]
The y-determinant is the determinant of the matrix [tex]A_y[/tex], this matrix is formed substituting in the matrix A the coefficients of y with the constant terms.
[tex]A_y=\left[\begin{array}{cc}3&10\\4&4\end{array}\right][/tex]
[tex]det(A_y)=\left|\begin{array}{cc}3&10\\4&4\end{array}\right|=(3)(4)-(4)(10)=12-40=-28[/tex]
