Given the system of equations, match the following items.
2 x - y = 0 x + y = -3
a. [0 -1
-3 1]
b. [2 0
1 -3]
c. [2 -1
1 1]
x determint
y determint
system determent

  A.  x-determinant

  B.  y-determinant

  C.  system determinant

Step-by-step explanation:

The "augmented" matrix for the system is the system coefficient matrix with the constants added as an extra column on the right:

The x-determinant is the determinant of the system matrix after the x-coefficients have been replaced by the constants:

The y-determinant is the determinant of the system matrix after the y-coefficients have been replaced by the constants:

Of course, the system determinant is the determinant of the matrix of coefficients of the variables:

_____

Comment on these determinants

Cramer's rule tells you the solution to the system is ...

  x = (x-determinant)/(system determinant)

  y = (y-determinant)/(system determinant)

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