SOLUTION: I have been trying to find a condition about r and s in this system that would make it inconsistent, but the -3rz keeps tripping me up! here is the equation. x

SOLUTION: I have been trying to find a condition about r and s in this system that would make it inconsistent, but the -3rz keeps tripping me up! here is the equation. x - 2y + z = 2

Question 849796: I have been trying to find a condition about r and s in this system that would make it inconsistent, but the -3rz keeps tripping me up!
here is the equation.
x - 2y + z = 2
-x + 3y = 3 + s
x - 5y - 3rz = 1
thank you for helping!!
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Add eq.1 and 2 together,

4.
.
.
Add eq. 2 and 3 together.

5.
.
.
Multiply eq. 1 by -2,

6.
.
.
Compare eq. 6 with eq. 5,

When ,

This makes the left hand side equal.
So to be inconsistent, when the left hand sides are equal, the right hand sides are not equal.
The two right hand sides are,

and

Find the value of when they are equal,

So when and is equal to any number other than , the system is inconsistent.
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