# Math Help - Basic system of linear equations

1. ## 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?

2. 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?
If you multiply both sides of the second equation by 3, you'll see

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

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

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