Given the system of equations: 2x – y = –2 x = 14 + 2y what is the value of the system determinant? what is the value of the y−determinant? what is the value of the x−determinant? what is the solution to the system of equations?

ANSWER 1

The given system  of equations is:

Let us rewrite the second system to obtain,

We need to apply the Cramer's rule. So we write out the coefficient matrices to obtain:

The answer column is;

The value of the y-determinant is denoted by . To find this we replace the coefficient determinant with answer-column values in y-column to get,

Recall that,

If

then,

This implies that,

ANSWER 2

The value of the x-determinant is denoted by . To find this we replace the coefficient determinant with answer-column values in x-column to get,

This implies that,

ANSWER 3

To find the solution to the system of equations.

We need to find the determinant of the coefficient matrix.

This implies that,

Cramer's rule says that,

and

Therefore the solution is and  .