Why not just parameterize with your free variable z, and use it to describe x and y, instead of introducing t, u and everything else?
Find the general integer solution (x, y, z) to the pair of equations
3x + 4y + 7z = 1
5x + 9y + 2z = 3
Put t = x + y + 2z. Then we have;
3t + y + z = 1
5t + 4y - 8z = 3:
Eliminating y, we get 7t + 12z = 1.
I can't solve this last part. I don't know why, it should be so easy... It should be...
(t, z) = (-5 + 12u, 3 - 7u), u an arbitrary integer but I'm nowhere near that. I end up doing about 4 substitutions but it all goes in a mess.
Damn I'm gonna need to put in a lot of pre done stuff so this makes sense them...
This is previous questions which I have done and solved but just taken straight from the questions and answers.
First pic is solving one linear equation, 2nd slide is the solution.
3rd pic is solving a linear system.
Yes that's the method we have to use.
I have done a few of them, it's really quite a simple thing once you get the hang of it but I just can't get this one done...
Here's an example of a linear equation (not a system), to show you what's going on. (in attachment)
This is using the question from the first slide in my previous post.