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

smileycellist2

Answered question

2020-11-03

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?

Answer & Explanation

Yusuf Keller

Yusuf Keller

Skilled2020-11-04Added 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.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-08Added 2605 answers

Answer is given below (on video)

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