SOLUTION: Select the augmented matrix for the following system of equations. y+2=3x 1/4z=z-1 z-8=x/2

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Question 895038: Select the augmented matrix for the following system of equations.
y+2=3x
1/4z=z-1
z-8=x/2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You have equations with the 3 variables x, y, and z.
You want to write each equation in the form
Ax%2BBy%2BC=D
and then you will use the coefficients A, B, C and D to build that matrix.
y%2B2=3x <---> 3%2Ax-1%2Ay%2B0%2Az=2
%281%2F4%29z=z-1 <---> 0%2Ax%2B0%2Ay%2B%283%2F4%29%2Az=1
z-8=x%2F2%29 <---> %281%2F2%29%2Ax%2B0%2Ay-1%2Az=-8
So,
system%28y%2B2=3x%2C%281%2F4%29z=z-1%2Cz-8=x%2F2%29 --->
and your matrix could be
%28matrix%283%2C4%2C3%2C-1%2C0%2C2%2C0%2C0%2C3%2F4%2C1%2C1%2F2%2C0%2C-1%2C-8%29%29

NOTE: There are other options, because each equation has an infinite number of equivalent equations, and you could rearrange your equations in different order.
For example, you could have used %28-1%2F2%29%2Ax%2B0%2Ay%2B1%2Az=8 or 1%2Ax%2B0%2Ay-2%2Ax=-16 as an equation equivalent to z-8=x%2F2%29 ,
and you could have used the coefficients of that equation for the top line of the matrix instead of the bottom line.