Without graphing, classify each system of equations as independent, dependent, or inconsistent. (please help me with these two!! I'm slightly confused) {6y + 2x = 8 {12y + 4x = 4 and {2 - 0.25x = 0.5y {-1.5y = 1.5x - 3

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Without graphing, classify each system of equations as independent, dependent, or inconsistent. (please help me with these two!! I'm slightly confused) {6y + 2x = 8 {12y + 4x = 4 and {2 - 0.25x = 0.5y {-1.5y = 1.5x - 3

Algebra
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The easiest way to solve this is by solving the system of equations either by substitution or elimination. Let's take a look at the first one: 6y + 2x = 8 12y + 4x = 4 We can solve this by elimination if we multiply the top equation by -2 and then adding the two equations together. This will give us 0 + 0 = -12. This is not a true statement. The system if equations is inconsistent and therefore does not yield a solution. If there is no solution, then that means that these two lines are in fact parallel. Can you try to solve the second one yourself using the same process?
yes, but do I have to find a pattern for that one as well like with the first equation (being it multiplied by -2)?
In a manner of speaking yes. When solving by elimination, you want to multiply by a factor so that if you add the two equations together, either the x's or the y's cancel. In the first set, multiplying by -2 and adding cancelled out both the x's AND the y's.

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im sorry for being a pain, but i would rearrange this equation so I can subtract/eliminate it, correct?
Yes, it would certainly make it easier :) 0.5y = 2- 0.25x -1.5y = 1.5x -3 It seems easier to cancel out the y. You don't have to multiply by a negative because they are already opposite signs. Try to do the rest and let me know if you're still having trouble :)
Study tool for later. @pokiedokie
thank you very much!! this is helpful
@CShrix i got -1y = -1.25-1, did i mess up somewhere because this doesn't seem correct to me?
You have to multiply the first equation by 3 first. Then when you add the two equations, there are no more y's in the equation. Then solve for x from there :)
1.5y = 6 - 0.75x -1.5y - 3 - 1.5x ________________ y = 3 - (-0.75) ??
1.5y-1.5y = 0. So you have 0 = 3 + 0.75x
whoops, sorry, so this would be inconsistent
thank you so much!!

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