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system of equations. what are the ordered triples?

0 votes

2x - y - z = -1

3x + y - z = 2

x + y - 5z = -8

system of equations. what are the ordered triples?

asked Oct 7, 2018 in ALGEBRA 2 by anonymous

1 Answer

0 votes

The System of Equations are

2x - y - z  =  - 1 --------------------> (1)

3x + y - z  =  2  --------------------> (2)

x + y - 5z  =  - 8  --------------------> (3)

Add Equations (1) and (2)

2x - y - z  =  - 1

3x + y - z  =  2

-----------------------

5x + 0 - 2z  =  1

5x - 2z  =  1 --------------> (4)

Add Equations (1) and (3)

2x - y - z  =  - 1 

x + y - 5z  =  - 8

---------------------

3x + 0 - 6z  =  - 9

3x - 6z  = - 9--------------> (5)

Multiply Eq (4) with 3 and subtract Eq (5) from it

Eq (4) X 3 =======>  15x - 6z  =  3

Eq (5) ==========>    3x - 6z  = - 9

                                    (-)   (+)     (+)

                                ----------------------------

                                       12x  =  12

                                           x  =  12/12

                                           x  =  1

Substitute x = 1 in Eq (4)

5(1) - 2z  =  1 

5 - 2z  =  1 

5 - 1  =  2z

4  =  2z

z  =  4/2

z  = 2

Substitute x = 1 and z  =  2 in Eq (1)

2(1) - y - 2  =  - 1

2 - y - 2  =  - 1

-y  =  -1

y  =  1

Answer :

The solutions are x = 1, y  =  1 and z = 2

Ordered Triplet is (1, 1, 2).

answered Oct 10, 2018 by homeworkhelp Mentor

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