Question 1799
these are just simultaneous equations...3 unknowns and 3 equations...solvable, if tedious.

You need to start with 2 equations and get rid of 1 variable...looking at the 3 equations, use 1 and 3, as they both have a y, so easy to remove these...

1 is {{{ x + y +  z = 6}}}
3 is {{{2x - y + 3z = 5}}}

the y's have Different signs so aDD (note the DD). Similarly, Same signs, then Subtract!!

so, we get equation 4

{{{3x + 4z = 11}}}

Now repeat the process with 2 other equations, say 2 and 3

{{{3x + 4y - 7z = 1}}}
{{{2x -  y + 3z = 5}}}

Again I will choose to get rid of the y term, but i need to increase the lower equation by a factor of 4, to get the 2 equations to match....

{{{3x + 4y -  7z =  1}}}
{{{8x - 4y + 12z = 20}}}

The y-terms have Different signs therefore we aDD, getting equation 5...

{{{11x + 5z = 21}}}

Now we use 4 and 5 to get rid of another variable...i choose to remove the z's, by making them both 20z...

equation 4 needs to be multiplied by 5: {{{ 3x + 4z = 11}}}
equation 5 needs to be multiplied by 4: {{{11x + 5z = 21}}} 

This gives us

{{{15x + 20z = 55}}}
{{{44x + 20z = 84}}}

Here the z terms have the Same sign therefore we Subtract the 2 equations, giving us {{{(-29x)=(-29)}}}, so x=1.

We now substitute this into 4 or 5, to find z (z=2) and then these into equation 1, 2 or 3 to find y (y=3).

THEN you double check each of the original equations (1, 2 and 3) to make sure that your answers are correct.



cheers
Jon.