solve the system of equations. Write the solution as an ordered triple.?

-2x + 2y - 10z = -14

x - y + 5z = 7

5x - 5y + 25z = 35

Put into a matrix:

-2 2 -10 | -14

1 -1 5 | 7

5 -5 25 | 35

Switch Row1 with Row2:

1 -1 5 | 7

-2 2 -10 | -14

5 -5 25 | 35

Let Row2 = Row2 + 2*Row1:

1 -1 5 | 7

0 0 0 | 0

5 -5 25 | 35

Let Row3 = Row3 - 5*Row1:

1 -1 5 | 7

0 0 0 | 0

0 0 0 | 0

The matrix is reduced to:

x y z

1 -1 5 | 7

Taking the equation out of the matrix, we have:

x - y + 5z = 7

Solving for x:

x = 7 + y - 5z...where y and z are any real numbers. That means there are an infinite number of solutions.

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Here is an example. Let y = 5 and z = 3. (These are just random numbers I chose.) In this case, x = -3. So...(x, y, z) = ( -3, 5, 3).

Check it:

-2(-3) + 2(5) - 10(3) = -14

(-3) - (5) + 5(3) = 7

5(-3) - 5(5) + 25(3) = 35

So, basically, just choose two random numbers for y and z, and plug these into the equation x = 7 + y - 5z to find the value of x.

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turn X, Y, Z a single variable like n. x + y + z = 6 2x + 4y + 2z = 24 -x + 8y - 3z = 36 n + n + n = 6 2n + 4n + 2n = 24 -n + 8n - 3n = 36 3n = 6 8n = 24 4n = 36 n = 2 n = 3 n = 9

- 2x + 2y - 10z = -14 ............................................ [1]

x - y + 5z = 7, ===> 2x - 2y + 10z = -14 ............................ [2]

5x - 5y + 25z = 35 .......................................................... [3

Add [1] & [2], 0 = -14 -14 = -28 ........... Not Possible.

Hence,

NO Solution ............................. ?????????? >===============< ANSWER

Seems like the something is wrong in the equation. There is no solution to these equations. So cannot be solved unless the question is correct. Re-check you question and update in additional details.