# Thread: Linear equations with letter variables

1. ## Linear equations with letter variables

Hey everyone, I have 4 questions which I know is a lot to ask but would really appreciate the answers to. Just open the link and click to zoom.
Thanks!

http://img251.yfrog.com/img251/56/15671906.png

2. 17. The system is consistent as long as the equations are not scalar multiples of each other.

Notice that the first row:

$2x + 3y = h$

is the same as

$4x + 6y = 2h$.

So we can not let $2h = 7$.

What value of $h$ can we not have?

Then what values of $h$ can we have?

3. 18.

Equation 1 is

$x - 3y = -2$

which is the same as

$5x - 15y = -10$.

The two equations are not scalar multiples of each other, so you can have $h$ be whatever you like.

4. Originally Posted by Prove It
17. The system is consistent as long as the equations are not scalar multiples of each other.
That's not exactly true. The system is consistent as long as no equation is a linear combination of the others- that may be what you meant by "scalar multiples". Certainly, if one is a multiple of another, that is a "linear combination". so it works for this problem.

Notice that the first row:

$2x + 3y = h$

is the same as

$4x + 6y = 2h$.

So we can not let $2h = 7$.

What value of $h$ can we not have?

Then what values of $h$ can we have?