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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- Dec 12th 2009, 08:42 PMcognoscenteBasic 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? - Dec 12th 2009, 09:07 PMProve It
If you multiply both sides of the second equation by 3, you'll see

$\displaystyle 3x + 4y = 12$

$\displaystyle 3x + 3ky = 12$.

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

That means $\displaystyle 3k = 4$ and so $\displaystyle k = \frac{4}{3}$.