How would I solve this system of equations?

Question

Here's a problem that I kind of got stuck on and I was wondering if someone can show me how to get the answer. Thank you :)

system of equations:
5x-8y+z=1
3x-2y+4z=3
10x-16y+2z=3

Answer 1

The best way to tackle this is to rewrite the first question so that it is in the form z = something.

5x - 8y + z = 1
Subtract 5x from both sides:
-8y + z = 1 - 5x
Add 8y to both sides:

z = 1 - 5x + 8y

Now put this value for z into the other two equations. This will give you two equations, each with only x and y in them. z has been eliminated.

Next rewrite one of these so that it is in the form y = something. Use this value for y in the third equation to get a single equation which just has x in it.

Finally solve this to find out what x is. Put this into the equation for y to find out what y is. Put the values for x and y into the equation for z to find out what z is.

Answer 2

Cannot solve since equations 1 and 3 contradict each other.

If 5x-8y+z=1, then 10x-16y+2z=2
But equation 3 states that 10x-16y+2z=3!

Answer 3

We have a problem!
If first equation is multiplied by 2:-
10x - 16y + 2z = 2

But 3rd equation gives:-
10x - 16y + 2z = 3

???????!

Answer 4

5x-8y+z=1.....(1)
3x-2y+4z=3...(2)
10x-16y+2z=3...(3)

(2)-[(1)*4]

-17x-34y=-1
x+2y=1/17

(3)-[(1)*2]

0=1 ..... Contradiction?

So you should doublecheck this problem...