Solving 2x2 and 3x3 Systems Using Cramer's Rule

A linear system is called:

consistent if it has at least one solution. In particular it is independent if it has exactly one solution and dependent if it has infinitely many solutions.
inconsistent if it has no solutions.

Cramer's Rule

Given a system

linear equations for

unknowns, if the determinant

of the matrix

is nonzero, the system has a unique solution, given by:

where

are the determinants of the matrices obtained by replacing the

-th column of

with the column vector

Write the following system in matrix form, then determine whether it can be solved using the Cramer's Rule.

Which value of parameter makes the following system independent?

Solve the following system using the Cramer's Rule.

If applicable, solve the system using Cramer's Rule, given: and

Solve the following system using the Cramer's Rule.

If applicable, solve the system using the Cramer's Rule, given: and