Question

What is the solution of the following system?

-2x - y = 1
-4x - 2y = -1
A. infinitely many solutions
B. no solutions
C. (3, 8)
D. (–3, –8)

Answer 1

Answer: B) no solutions

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Step-by-step explanation:

Let's isolate the variable y in the first equation

-2x - y = 1

-2x = 1 + y

1+y = -2x

y = -2x-1

Then we'll plug this into the second equation

-4x - 2y = -1

-4x - 2(-2x-1) = -1

-4x + 4x + 2 = -1

0x + 2 = -1

0 + 2 = -1

2 = -1

We run into a contradiction. No matter what x value we pick, the last equation will never be true. This leads to a domino effect to cause the first set of original equations to never be true when considered as a system.

Therefore, this system is inconsistent. There are no solutions. These two lines graph out parallel lines that never intersect.