Question 965464
3 equations need to be solved simultaneously.


the equations are:


x + y - 2z = 5 (e1)
x + z = 4 (e2)
y - z = 6 (e3


subtract e2 from e1 to get:


x + y - 2z = 5 minus:
x + 0 + z = 4 becomes:
0 + 6 - 3z = 1


the result of the operation is y - 3z = 1 (e4).


take e3 and e4 and solve them simultaneously for either y or z.


the equations are:


y - z = 6 (e3)
y - 3z = 1 (e4)


subtract e4 from e3 to get:


2z = 5


solve for z to get z = 2.5


in e3, if z = 2.5, then y - z = 6 becomes y - 2.5 = 6 which becomes y = 8.5.


in e1, if z = 2.5 and y = 8.5, then x + y - 2z = 5 becomes x + 8.5 - 2 * 2.5 = 5 becomes x + 3.5 = 5 which becomes x = 1.5


if all was done correctly, your solution should be:


x = 1.5
y = 8.5
z = 2.5


let's see if that's true.
it has to be true in all 3 equations.


the original 3 equations are:


x + y - 2z = 5 (e1)
x + z = 4 (e2)
y - z = 6 (e3)


when x = 1.5 and y = 8.5 and z = 2.5, these equations become:


1.5 + 8.5 - (2 * 2.5) = 5 (e1) which becomes 5 = 5 which is true.
1.5 + 2.5 = 4 (e2) which becomes 4 = 4 which is true.
8.5 - 2.5 = 6 (e3) which becomes 6 = 6 which is true.


all 3 equations are true, so the solution is good.


x = 1.5
y = 8.5
z = 2.5