Basic system of linear equations

I need to determine a value of K for which the system has infinity many solutions

3x+4y=12
x+ky=4

Then

x=4-(4/3)y

4-(4/3)y+ky=4
-(4/3)y+ky=0

So if k=4/3, then y=y?

Quote:

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Originally Posted by cognoscente

I need to determine a value of K for which the system has infinity many solutions

3x+4y=12
x+ky=4

Then

x=4-(4/3)y

4-(4/3)y+ky=4
-(4/3)y+ky=0

So if k=4/3, then y=y?

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If you multiply both sides of the second equation by 3, you'll see


.

For the system to have infinitely many solutions, the equations would have to be identically equal.

That means and so .