Part (a)

The given system of equation is

3x−6y=−12

x−2y=−8

Substitute x=−8+2y in 3x−6y=−12 and solve as follows.

3(−8+2y)−6y=−12

−24+6y−6y=−12

−24+0=−12

−24=−12

A contradiction

Thus, there is no solution for the given system of equations.

Part (b)

Look at the system of equations

3x−6y=−12

x−2y=−8.

Rewrite it as x−2y=−4 (divided by 3).

x−2y=−8

Note that two equations differs only by a constant.

Therefore, the given equations are parallel lines.

The given system of equation is

3x−6y=−12

x−2y=−8

Substitute x=−8+2y in 3x−6y=−12 and solve as follows.

3(−8+2y)−6y=−12

−24+6y−6y=−12

−24+0=−12

−24=−12

A contradiction

Thus, there is no solution for the given system of equations.

Part (b)

Look at the system of equations

3x−6y=−12

x−2y=−8.

Rewrite it as x−2y=−4 (divided by 3).

x−2y=−8

Note that two equations differs only by a constant.

Therefore, the given equations are parallel lines.