SOLUTION: I'm trying to classify the system and determine the number solutions without graphing -5x-2y=10 -10x-4y=20 A. Consistent, dependent B. consistent , independent C. Inconsiste

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Question 605884: I'm trying to classify the system and determine the number solutions without graphing
-5x-2y=10
-10x-4y=20
A. Consistent, dependent
B. consistent , independent
C. Inconsistent
D. None of these
Email llthomas83@yahoo.com
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let z = -5x-2y

Notice that 2z = 2(-5x-2y) = -10x-4y

So we can replace the left hand side of the first equation with 'z'. We can also replace the left hand side of the second equation with '2z'

This gives us the equations

z = 10
2z = 20

If we solve the second equation for z, we do indeed get z = 10.

This tells us that there are an infinite number of solutions. This is because the system we're given basically boils down to -5x-2y=10, which has an infinite number of solutions.

So this means that the system is consistent and dependent.