## gaussian elimination

I need a math guru to explain why and how the elimination method of solving simultaneous equations works ?

why do we add or subtract the two equations ?(I undertand in order to eradicate either term) but I need to know from the basics .

For that matter, how/why does the substitution method work ?

thanks

Roger
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 Quote by roger I need a math guru to explain why and how the elimination method of solving simultaneous equations works ? why do we add or subtract the two equations ?(I undertand in order to eradicate either term) but I need to know from the basics . For that matter, how/why does the substitution method work ? thanks Roger
The answer really goes back to the nature of "=". Think of it as weighing things on balance scale. If, when you put A on one side and B on the other, if they balance, then A= B (that is, A and B weigh the same). If you add the same weight on both sides, they still balance. If you take the same weight from both sides, they still balance.

If I know that x+ y= 10 then adding x+ y to one side of any equation is the same as adding "10". In particular, if I also know that x- y= 6, then
adding x+ y to x- y gives me 2x. Adding 10 to 6 gives me 16 and that's STILL the same thing: 2x= 16 so I must have x= 8.

Long, long ago, you learned "if you do the same thing to both sides of an equation, you still have a true equation". It's still true!
 Recognitions: Gold Member Homework Help Science Advisor roger: Note that, just as with the scales, a balance can be sustained even if the weight on a single side has changed (as long as the weight on the other side also has changed accordingly). It is the condition that the weights on BOTH scales are EQUAL which keeps the balance; the particular value of that shared weight has no bearing on the balancing.

## gaussian elimination

 Quote by HallsofIvy The answer really goes back to the nature of "=". Think of it as weighing things on balance scale. If, when you put A on one side and B on the other, if they balance, then A= B (that is, A and B weigh the same). If you add the same weight on both sides, they still balance. If you take the same weight from both sides, they still balance. If I know that x+ y= 10 then adding x+ y to one side of any equation is the same as adding "10". In particular, if I also know that x- y= 6, then adding x+ y to x- y gives me 2x. Adding 10 to 6 gives me 16 and that's STILL the same thing: 2x= 16 so I must have x= 8. Long, long ago, you learned "if you do the same thing to both sides of an equation, you still have a true equation". It's still true!
What about the fact that the addition of the equation makes the y disappear, is that an optical illusion, or a false alarm ?

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$x-y=7;y=3$.Consider the first equation:$x-y=7$.Add on both sides "y".U'll get:$x-y+y=7+y$.Reduce "y" in the LHS and you're left with:$x=7+y$.Use the second equation to get:$x=7+3=10$.