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?

smileycellist2 2020-11-03 Answered
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?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Yusuf Keller
Answered 2020-11-04 Author has 90 answers
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.
Did you like this example?
Subscribe for all access
Jeffrey Jordon
Answered 2021-11-08 Author has 2581 answers

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more