Question

PLEASE PLEASE HELP!!!!

Answer 1

For your first question the answer is C(-2) and your next question the answer is A(-28)

Answer 2

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.

$A=\left[\begin{array}{cc}1&1\\1&-1\end{array}\right]$

In the 2x2 matrix, the determinant is calculated by obtaining the difference between the diagonally down product and the diagonally up product.

$det(A)=\left|\begin{array}{cc}1&1\\1&-1\end{array}\right|=(1)(-1)-(1)(1)=-1-1=-2$

The y-determinant is the determinant of the matrix $A_y$, this matrix is formed substituting in the matrix A the coefficients of y with the constant terms.

$A_y=\left[\begin{array}{cc}3&10\\4&4\end{array}\right]$

$det(A_y)=\left|\begin{array}{cc}3&10\\4&4\end{array}\right|=(3)(4)-(4)(10)=12-40=-28$