Question

Is the following system consistent or inconsistent?
8x + y + 4 = 0

y = -8x - 4

Answer 1

re arrange the first equation... if once you rearrange to have y on one side and the rest of the parts on the other..compare to the second equation..
if they look the same then they are consistent...

Answer 2

Alternatively, plug in y = -8x - 4 into 8x + y + 4 = 0 to get

8x + y + 4 = 0

8x + (-8x - 4 + 4 = 0

8x - 8x - 4 + 4 = 0

I'm sure you see what the answer is from here

Answer 3

So then it is consistent?

Answer 4

yep, if you simplify fully, you'll get 0 = 0

That means you'll have infinitely many solutions, which makes the system consistent

Answer 5

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Answer 6

yw