I don't get it

Does anyone know of any interactive/good visual website for the adding and subtracting of planes? I'm doing the intersection of 2 planes right now, and I was just wondering if you had 2 cartesian eq'ns say 5x+2y+7z+1=0 and 5x-6y+8z-1=0, if you minus the 2 equations you'll have eliminated x, and you'll get a line equation with only y and z as the variables. I'm just trying to get a visual idea of what's going on when you eliminate a variable from 2 cartesian equations. So originally you had two different planes, now that you subtracted one from the other, what does the new line represent? If any one can help explain it/provide visual that would be greatly appreciated.
 
The line represents where the two planes intersect.
 
The line represents where the two planes intersect.
That's what my friend was saying too, but how do you know that?
Whats the difference between eliminating, x or y or z in 2 cartesian equations and the line it creates?
 
That's what my friend was saying too, but how do you know that?
Whats the difference between eliminating, x or y or z in 2 cartesian equations and the line it creates?
You can only subtract if both equations are true. The only way both equations are true is if they intersect.
 
You can only subtract if both equations are true. The only way both equations are true is if they intersect.
But you can still subtract them and get a solution of 0, which means they don't intersect (the 2 planes are parallel)?

Do you know what this type of math is called? I just can't seem to get my head wrapped around the subtraction of planes...maybe an animation/diagram would help? I mean, I understand 2 functions adding/subtracting because you can see the product visually and how its dependent on the 2 equations. With planes, it's harder to visualize since it's in 3d :(

Thanks for you help though!
 
But you can still subtract them and get a solution of 0, which means they don't intersect (the 2 planes are parallel)?

Do you know what this type of math is called? I just can't seem to get my head wrapped around the subtraction of planes...maybe an animation/diagram would help? I mean, I understand 2 functions adding/subtracting because you can see the product visually and how its dependent on the 2 equations. With planes, it's harder to visualize since it's in 3d :(

Thanks for you help though!
If you subtract the two planes and get zero then they are parallel. Parallel planes don't need to intersect but in that case you won't get zero, you'll get something that doesn't make scene like 0=1. The type of math is called linear algebra. The type method is called elimination.
 

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