# Thread: Understanding Systems of Three Equations in Three Variables (1)

1. ## Understanding Systems of Three Equations in Three Variables (1)

Determine whether the ordered triple is a solution of the system.

6x-y+4z=4
-2x+y-z=5
2x-3y+z=2

(-1/2, -3,1)

My answers are:
x= 7 5/14 or 103/14
y=4
z= 5/7

So no, the ordered triple is not a solution of the system.

Are my answers for the variables correct?

2. ## Re: Understanding Systems of Three Equations in Three Variables (1)

If the answers for (x,y,z) is not asked, you can easily check by substituting values to the three equations. Then you can see the given ordered triple satisfy only the first equation. So the given ordered triple is not the solution.

Anyhow, your answers does not seems to be correct. Because it does not satisfy the above three equations when substituted and you cannot get two answers since there should only be one point which satisfies this system of equations.

correct answer is (-69/4,-7/2,26)

3. ## Re: Understanding Systems of Three Equations in Three Variables (1)

Originally Posted by Kibbygirl
-2x+y-z=5
2x-3y+z=2
Kibby, I suggest you learn how to solve such systems...else you'll fall behind.
As example, you can add together the above 2 equations to get:
-2y = 7
y = -7/2
But they're not always that easy!

4. ## Re: Understanding Systems of Three Equations in Three Variables (1)

We're being taught to do three equations to solve for three variables. He wants us using elimination process, showing our work. By doing elimination, he wants us to find the value of the variables. First eliminating 1 variable in two equations, then using those "solutions" to eliminate one of the other remaining variables. And then plugging in the two found values of two variables to solve for the last unknown variable. I follow the example he gave us and just plugged in the questions information/numbers. So I am completely confused on what I did wrong...