mariomintchev
5x+5y=1
25x+ky=4
solve for k
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Kuoministers
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there is few ways of working this out. Elimination, Substitution and maybe multiplication
Kuoministers
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which way do you prefer?
mariomintchev
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i need my mind refreshed. whichever method works best is the method i choose.
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ill use substitution then :P
x = \[x = y - \frac{ 1 }{ 5 }\]
25x + ky = 4
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25(y - \[25(y - \frac{ 1 }{ 5 }) + ky = 4\]
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\[25y - 5 + ky = 4\]
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do you get it now?
mariomintchev
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howd u get y-(1/5)?
Kuoministers
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divide everything in the first equation by 5
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there is no solution :)
Kuoministers
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ill use elimination now
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times the first equation by -5
-25x - 25y = -5
25x + ky = 4
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now add this equation vertically together.
it would give you k=25
mariomintchev
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i probably shoulda phrased the question the way they have it on my hw.
it says:
Determine the value of k for which the system of linear equations has no solutions.
Kuoministers
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haha great :/
u say that now
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you know why there is no solution?
if you sub K = 25 it wont work
mariomintchev
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:(
mariomintchev
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yes?
mariomintchev
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because they equal different things
Kuoministers
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\[\Huge{\color{Purple}{\\{\
\boxed{\mathbb{\text{}{}}{\color{green}{\color{blue}T{\color{purple}h{\color{pink}a{\color{red}nk}}}}}}}}} \]
\[\Huge{\color{Purple}{\\{\
\boxed{\mathbb{\text{}{}}{\color{blue}Y{\color{green}o{\color{red}u}}}}}}} \]
mariomintchev
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haha no, THANK YOU ! :)
mariomintchev
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ok i have another one lol
this one wants the k to have an infinite amount of solutions
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49x-49y=49
7x+ky=7
mariomintchev
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the answer is not 1,7,49,1/7, or 1/49.
mariomintchev
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@Kuoministers
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sorry been bit busy
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so do you have an idea where to start?
Kuoministers
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i would times the 2nd equation by 7
mariomintchev
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ok...
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do you undertand this yet lol?
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49x-49y=49
7x+ky=7
49x-49y=49
49x + 7ky = 49
mariomintchev
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dont know where to go from there
Kuoministers
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-49y - 7ky = 0
-7y(7 + k) = 0
mariomintchev
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how do we get the k from that
Kuoministers
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im bit confused :P
you sure their is more than 1 answer??
mariomintchev
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its 1 answer
Kuoministers
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oh u said
this one wants the k to have an infinite amount of solutions
mariomintchev
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1 K but infinite solutions
we need the K
Kuoministers
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y(7 + k ) = 0
from this can you find K?
im pretty sure you can :P
Kuoministers
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hint: you only need to look at this question to get K
mariomintchev
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ok its -7 lol
mariomintchev
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im feeling slooow ha
Kuoministers
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ok i g2g now :)
Kuoministers
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have fun with your maths
mariomintchev
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haha see ya.