Solve each system using Gaussian elimination. State whether each system is independent, dependent, or inconsistent.

Question

x - y = 2
3x - y =12

Answer 1

Gaussian Elimination method :

The linear equations are x  - y = 2 and 3x  - y = 12 .

Write the equations into matrix form AX = D .

A  is coefficient matrix , X  is variable matrix and D  is Constant matrix.

The augmented matrix is [AD ]

Here represents first row and represents second row.

The solution is .

The system of equation has exactly one solution, so the system is consistent and independent.