Question

PLEASE PLEASE HELP!!!!

Given the system of equations, what is the value of the system determinant?
x + y = 8
x - y = 10

A. 0
B. -1
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
B. -14
C. 28

Answer 1

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

Answer 2

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

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`