Question 83597
1.
*[invoke calculating_slope 1, 2, -3, 6]


2.

Start with the given system and label the equations

{{{x + y - z = 0}}} Equation 1
{{{2x - y + z = 6}}} Equation 2
{{{-x + y + z = 8}}} Equation 3
{{{3x=6}}} Add equations 1 and 2
{{{x=2}}} Divide both sides by 3


Now lets use this info to find another variable


{{{2*2-y+z=6}}} Plug in x=2 into equation 2 to get Equation 4
{{{4-y+z=6}}} Multiply
{{{-2+y+z=8}}} Plug in x=2 into equation 3 to get Equation 5
{{{-(-2+y+z)=-8}}} Multiply equation 3 by -1


So now we have the equations

{{{4-y+z=6}}} Equation 4
{{{2-y-z=-8}}} Equation 5
{{{6-2y=-2}}} Add equations 4 and 5
{{{-2y=-8}}} Subtract 6 from both sides
{{{y=4}}} Divide both sides by -2


Now lets use this to find z


{{{2+4-z=0}}} Plug in x=2 and y=4 into Equation 1 (at this point any equation will do)
{{{6-z=0}}} Add
{{{-z=-6}}} Subtract
{{{z=6}}} Divide


So our solution is 

(2,4,6)