which ordered triple represents all of the solutions to the system of equations shown below?
2x ­- 2y ­- z = 6
­-x + y + 3z = -­3
3x ­- 3y + 2z = 9
a(­-x, x + 2, 0)
b(x, x ­- 3, 0)
c(x + 2, x, 0)
d(0, y, y + 4)
what is the solution to the system of equations shown below?
2x -­ y + z = 4
4x ­- 2y + 2z = 8
­-x + 3y ­- z = 5
a (5, 4, -­2)
b (0, ­-5, ­-1)
c no solution
d infinite solutions

Step-by-step explanation:

1. A graphing calculator or any of several solvers available on the internet can tell you the reduced row-echelon form of the augmented matrix ...

is the matrix ...

The first row can be interpreted as the equation ...

  x -y = 3

  x -3 = y . . . . . add y-3

The second row can be interpreted as the equation ...

  z = 0

Then the solution set is ...

  (x, y, z) = (x, x -3, 0) . . . . matches selection B

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2. The second equation is 2 times the first equation, so the system of equations is dependent. There are infinite solutions.

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