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Find the value of k, so that the following system is consistent:

 

x + y = 1

kx + y = 2

x + ky = 3

 Jun 18, 2020
 #1
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+1

So, we know that kx + y = 2.

Dividing everything by k, we get x + y/k = 2/k

 

Let's go to the first equation for a moment - this is x + y = 1.

Dividing everything by k, we get x/k + y/k = 1/k.

 

x + y/k = 2/k

x/k + y/k = 1/k

 

x - x/k = 1/k

Try this!

 Jun 18, 2020
 #2
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-1

Okay...

 

First, we isolate x+y=1 into

 

x=1-y

 

Then we isolate k into

 

k(1-y)+y=2

 

Which gets us k=(2-y)/(1-y)

Now we know that y can't be 1

 

We then isolate y.

 

1-y+(2-y)/(1-y)=3

 

Y is 2/3

 

Substitude 2/3

 

And we get... k=4

 

Substitude AGAIN and we get x=1/3

 

BABABABOWWWW!

 

Yay!
 

Edit:

It's not that I'm sensitive, but I really need to know the point of downvoting someone... am I wrong lol?

 Jun 18, 2020
edited by Varxaax  Jun 18, 2020

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