Question 1194003: hello! I tried my best to input the question, I'm unsure if there is a better way to type out the matrix portion of the question but I hope its readable (The brackets are meant to be connected). any help is appreciated! thank you
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The following augmented matrix is in row-echelon form and represents a linear system. Solve the system by using back-substitution, if possible.
[1 3| 6]
[0 1| -1]
What is the solution to the linear system?
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
The bottom row of 0, 1, -1 tells us we have the equation 0x + 1y = -1
That leads to y = -1
The top row of 1, 3, 6 tells us we have the equation 1x+3y = 6 or simply x+3y = 6
Plug in y = -1 and solve for x.
This is the back-substitution portion.
Substitution because we replace y with -1
The "back" part refers to us going back up the matrix.
x+3y = 6
x+3(-1) = 6
x-3 = 6
x-3+3 = 6+3
x = 9
The solution is (x,y) = (9, -1)
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