solve the system of equations.If the system has no solution,say that it is inconsistent.

Question

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> solve the system of equations.If the system has no solution,say that it is inconsistent.

Answer 1

Step 1:

The system of equations are .

To eliminate the y value add the equations (2) and (3).

                                    

Multiple each side of the equation (1) by 2 .

Add the above equation with equation (2).

Step 2:

Subtract the equation (4) from equation (5).

The original system is equivalent to a system containing two equations.

Therefore the equations are dependent and the system has infinitely many solutions.

Now solve the equation (4) for x.

Substitute   in equation (1).

Solution:

.