If the equations are parallel but not the same they must be paralle, but not on top of each other. Rule 2: If the slopes (the 'm's) are the same, and the intercepts (the 'c's) are the same also, the system is dependent. If they are on top of each other, the equations will be the same, so they will also have the same intercept (the 'c'). If the slopes are the same, the lines must either be on top of each other, or parallel. Rule 1: If the slopes (the 'm's) are different, the system is independent (and therefore also consistent) It might be at a huge value of x or y, but they will meet! So:

That means that the two lines are not parallel, and so they must meet eventually.

If the coefficients (the 'm's) are different, that means the slopes are different. But that's great for this example, can we make a general rule? Sure can! Let's convert Eq1:Īha! This looks suspicious! We have THE SAME EQUATION TWICE! So this system is dependant and consistent. It doesn't matter which, but let's get them into y = mx + c form. Please sign in to leave a comment.It all becomes clear if they are in the same form. So i see what he means i LOVE KA but i get side-tracked way too often :D It definitely needs to be clear though what we need to do first because maths is a very step-by-step process and we need a smooth process to keep going on a mostly smooth path, it's mainly what's made me see something as very hard to understand and i end up spending hours sifting through the info trying to get things straight for myself lol it's painful to say the least but i don't want it to keep occuring, it's already a lot of work going over it all then the practise i put in.

I've gotten caught out like this a couple times doing the earlier grades as well too hard too quickly (or so it seems) but i know it's not going to change quickly either so if i get this in future i know i need to get it straight which concepts i should learn first and if it makes me go too far then i then eventually backtrack to where i need to be and what i need to work on first.

Khan academy systems of equations