Thread: Solving system of equations

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.

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?

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.

do you have to solve it with that method? I know there are teachers that want it solved with a particular method sometimes, so is that the case here? if not, why not solve it another way?

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.