Question 1194064: The following augmented matrix is in row echelon form and represents a linear system. Use back-substitution to solve the system if possible.
[1 1 -1|2]
[0 1 -1|2]
[0 0 1|1]
What is the solution to the linear system?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
The bottom row indicates we have this equation
0x+0y+1z = 1
which simplifies to
z = 1
The middle row says
0x+1y+(-1)z = 2
which simplifies to
y-z = 2
Plug in z = 1 and solve for y
y-z = 2
y-1 = 2
y = 2+1
y = 3
The first line of the given augmented matrix says we have this equation
1x+1y+(-1)z = 2
aka
x+y-z = 2
Plug in y = 3 and z = 1. Solve for x.
x+y-z = 2
x+3-1 = 2
x+2 = 2
x = 2-2
x = 0
Solution:
x = 0, y = 3, z = 1
We can condense this into the ordered triple (x,y,z) = (0,3,1)
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