1. Interchange two equations

2. Multiply an equation by a nonzero constant

3. Add a multiple of an equation (equation 1) to another equation (equation 2) and replace the second equation (say equation 2) with the result.

Now that I have listed what I must work off of, the first problem I am having is with this system...

\(\displaystyle (\cos\theta)x + (\sin\theta)y = 1\)

\(\displaystyle (-\sin\theta)x + (\cos\theta)y = 1\)

I need to solve this system for x and y. I do know that my answer will more than likely be in terms of sines and cosines.

The second problem I am uncertain about is this:

kx + y = 4

2x - 3y = -12

I need to find the value(s) of k such that the system has an infinite number of solutions. I believe my answer of k = -2/3 is accurate and as far as I can tell with k being -2/3 the system has an infinite number of solutions. However, I am uncertain if there are other values of k which would give me the same answer. I apologize if this should be in a different forum, but as my class is Elementary Linear Algebra I figured this location was appropriate. Thanks for all your help.