Question

Please help!!!

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

Answer 1

1. b (x, x ­- 3, 0)
2. d Infinite Solutions

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 ...

`\left[\begin{array}ccc2&-2&-1&6\\-1&1&3&-3\\3&-3&2&9\end{array}\right]`

is the matrix ...

`\left[\begin{array}ccc1&-1&0&3\\0&0&1&0\\0&0&0&0\end{array}\right]`

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.