Question

What is the solution to the following system of equations? 3x-6y=-12 x-2y=-8 (a)Use the substitution method to justify that the given system of equations has no solution. (b)What do you know about the two lines in this system of equations?

Equations
What is the solution to the following system of equations?
3x-6y=-12
x-2y=-8
(a)Use the substitution method to justify that the given system of equations has no solution.
(b)What do you know about the two lines in this system of equations?

2020-11-04
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
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.