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

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Add eq.1 and 2 together,
y%2Bz=2%2B3%2Bs
4.y%2Bz=5%2Bs
.
.
Add eq. 2 and 3 together.
-2y-3rz=3%2Bs%2B1
5.-2y-3rz=4%2Bs
.
.
Multiply eq. 1 by -2,
-2y-2z=-2%285%2Bs%29
6.-2y-2z=-10-2s
.
.
Compare eq. 6 with eq. 5,
-2y-3rz=4%2Bs
When -2z=-3rz,
-2=-3r
r=2%2F3
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,
-10-2s
and
4%2Bs
Find the value of s when they are equal,
-10-2s=4%2Bs
-14=3s
s=-14%2F4
So when r=2%2F3 and s is equal to any number other than 14%2F3, the system is inconsistent.