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Mathematics 9 Online
OpenStudy (anonymous):

5x+5y=1 25x+ky=4 solve for k

OpenStudy (kuoministers):

there is few ways of working this out. Elimination, Substitution and maybe multiplication

OpenStudy (kuoministers):

which way do you prefer?

OpenStudy (anonymous):

i need my mind refreshed. whichever method works best is the method i choose.

OpenStudy (kuoministers):

ill use substitution then :P x = \[x = y - \frac{ 1 }{ 5 }\] 25x + ky = 4

OpenStudy (kuoministers):

25(y - \[25(y - \frac{ 1 }{ 5 }) + ky = 4\]

OpenStudy (kuoministers):

\[25y - 5 + ky = 4\]

OpenStudy (kuoministers):

do you get it now?

OpenStudy (anonymous):

howd u get y-(1/5)?

OpenStudy (kuoministers):

divide everything in the first equation by 5

OpenStudy (kuoministers):

there is no solution :)

OpenStudy (kuoministers):

ill use elimination now

OpenStudy (kuoministers):

times the first equation by -5 -25x - 25y = -5 25x + ky = 4

OpenStudy (kuoministers):

now add this equation vertically together. it would give you k=25

OpenStudy (anonymous):

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.

OpenStudy (kuoministers):

haha great :/ u say that now

OpenStudy (kuoministers):

you know why there is no solution? if you sub K = 25 it wont work

OpenStudy (anonymous):

:(

OpenStudy (anonymous):

yes?

OpenStudy (anonymous):

because they equal different things

OpenStudy (kuoministers):

\[\Huge{\color{Purple}{\\{\ \boxed{\mathbb{\text{}{}}{\color{green}{\color{blue}T{\color{purple}h{\color{pink}a{\color{red}nk}}}}}}}}} \] \[\Huge{\color{Purple}{\\{\ \boxed{\mathbb{\text{}{}}{\color{blue}Y{\color{green}o{\color{red}u}}}}}}} \]

OpenStudy (anonymous):

haha no, THANK YOU ! :)

OpenStudy (anonymous):

ok i have another one lol this one wants the k to have an infinite amount of solutions

OpenStudy (anonymous):

49x-49y=49 7x+ky=7

OpenStudy (anonymous):

the answer is not 1,7,49,1/7, or 1/49.

OpenStudy (anonymous):

@Kuoministers

OpenStudy (kuoministers):

sorry been bit busy

OpenStudy (kuoministers):

so do you have an idea where to start?

OpenStudy (kuoministers):

i would times the 2nd equation by 7

OpenStudy (anonymous):

ok...

OpenStudy (kuoministers):

do you undertand this yet lol?

OpenStudy (kuoministers):

49x-49y=49 7x+ky=7 49x-49y=49 49x + 7ky = 49

OpenStudy (anonymous):

dont know where to go from there

OpenStudy (kuoministers):

-49y - 7ky = 0 -7y(7 + k) = 0

OpenStudy (anonymous):

how do we get the k from that

OpenStudy (kuoministers):

im bit confused :P you sure their is more than 1 answer??

OpenStudy (anonymous):

its 1 answer

OpenStudy (kuoministers):

oh u said this one wants the k to have an infinite amount of solutions

OpenStudy (anonymous):

1 K but infinite solutions we need the K

OpenStudy (kuoministers):

y(7 + k ) = 0 from this can you find K? im pretty sure you can :P

OpenStudy (kuoministers):

hint: you only need to look at this question to get K

OpenStudy (anonymous):

ok its -7 lol

OpenStudy (anonymous):

im feeling slooow ha

OpenStudy (kuoministers):

ok i g2g now :)

OpenStudy (kuoministers):

have fun with your maths

OpenStudy (anonymous):

haha see ya.

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