Question

X+ y+ z = 4 2x+5y+2z = 26 −x+9y−3z = 52 ... Question content area right Part 1 Write the solution as an ordered triple. Select the correct choice below and fill in any answer boxes within your choice. A.There is one​ solution, enter your response here,enter your response here,enter your response here. ​(Type exact answers in simplified​ form.) B. The system is dependent. C. There is no solution.

Determine whether ​(−2​,−1​,2​) is a solution of the system. x+ y+z = −1 x−2y−z = −2 3x+3y−z = −11

Answer 1

• A. there is one solution: (x, y, z) = (-4, 6, 2)
• (-2, -1, 2) is the solution to the system

Explanation:

You want to know the solutions to the systems of equations ...

• x +y +z = 4
• 2x +5y +2z = 26
• -x +9y -3z = 52

and

• x +y +z = -1
• x -2y -z = -2
• 3x +3y -z = -11

Solutions

The solution to a set of linear equations is conveniently found by a calculator capable of reducing the augmented coefficient matrix to reduced row-echelon form. The variable values comprising the solution are found in the last column of the reduced matrix.

First system

The one solution is shown to be (x, y, z) = (-4, 6, 2).

Second system

The one solution is shown to be (x, y, z) = (-2, -1, 2). That is, the offered triple is a solution.

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Additional comment

There are other ways to solve these systems of equations: ad hoc methods, Cramer's Rule, graphing. It seems to make sense to use the calculator's ability to find the solution if you're going to use a calculator anyway.

The systems of equations can be reduced to a set of 2 equations in 2 variables by using substitution for one of the variables. The first equation can be used to write an expression for z, for example.

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