Linear Algebra - System of 2 Equations with 3 Variables-possible?

[chrisdapos]

Linear Algebra - System of 2 Equations with 3 Variables--possible?

Homework Statement

Solve: x1-3x2+4x3=-4
3x1-7x2+7x3=-8
-4x1+6x2-x3=7

The Attempt at a Solution

I was able to make it to:
1 -3 4 -4
0 -10 25 -11
0 0 0 0
So the third row goes away, and I am left with:
1 -3 4 -4
0 -10 25 -11
I am pretty sure that cannot be solved, or am I overlooking something? Thank you in advance!

 

[durt]

It looks like you have a free variable. So you can solve for the other two in terms of it.

 

[NateTG]

I am pretty sure that cannot be solved, or am I overlooking something? Thank you in advance!

The solution isn't unique, you can try plugging in a value for $x_1$ and solving the rest.
$$x_1=1,2,3,4,5,6...\pi, e,...$$

 

[proton]

whenever you have more unknowns than equations, you get infinitely many solutions and one or more variables become free varaibles

 

[NateTG]

whenever you have more unknowns than equations, you get infinitely many solutions and one or more variables become free varaibles

Sometimes there can still be zero solutions:
$$x+y+z=0$$
$$x+y+z=1$$