#For what values of h and k is the following system consistent?

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neon lagoonBOT
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sick raptor
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we can solve it without using determinents and all
simply multiply 1st equation by -3
you will notice they are parallel lines
unless they represent same line they are inconsistent

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so -3h=k

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thats the solution

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i hope i am right

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consider -3h = k

latent grove
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So do i not put it into an augmented matrix?

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and try to make it into echelon form?

sick raptor
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It's up to you, you can just divide the upper over the lower one and you'll have to solve x, after which you just fill the x and you'll get h, and after which you'll get k because it's a divisor

sick raptor
latent grove
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thats echelon form

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this is where im at

sick raptor
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check your calculation

latent grove
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which part is wrong?

sick raptor
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.

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or rather

latent grove
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isnt -3*-1 = 3

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then i added it to 3

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which give 6

sick raptor
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-3h - k sorry,

latent grove
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this problem is so confusing

sick raptor
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just write the second equation as -6x1 + 3x2 = -3h

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then divide the first over the second

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and it'll get rid of h

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and you'll have x to work with

latent grove
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ok ill try that

sick raptor
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sorry I'm working this all in my mind

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excuse me, try substraction instead of division

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division will only nullify the equation

latent grove
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alright will try now

sick raptor
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when two equations are the same or are only different by a multiplicative proportion, it will always end up by a self evident conclusion 0=0 or 1=1 etc..

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my bad

latent grove
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so would it be -8x1 + 4x2 = k - h

latent grove
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i dont think im allowed to just sbtract them

sick raptor
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okay

latent grove
sick raptor
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i'll leave this to someone else, I'll try first solving it on paper instead of speculating

latent grove
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ok

sick raptor
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for what seems is that the system is always consistent if k = -3xh

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the second line of the system is just useless

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it's a repetition of the first

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So you can just write the solution as the set S = {...(1,-3),(2,-6),(3,-9)...\} of course you won't write it like this I'm just giving you an idea

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unless you can give me more context

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@latent grove

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you will write the set S in terms of h and k belonging to R

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or x and y as solution tuples if you don't want to repeat h and k