What are the three variables

2x+y+7z=5

3x-2y-=-1

4x-y+3z=5

asked Oct 27, 2018 in ALGEBRA 2 by anonymous
reshown Oct 28, 2018 by bradely

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1 Answer

The Simultaneous Equations are

2x + y + 7z = 5 ----------------------> (1)

3x - 2y = -1 --------------------> (2)

4x - y + 3z = 5 -------------------------> (3)

Multiply Eq (1) with 3 and Eq (3) with 7 and subtract Eq (3) from Eq (1)

Eq (1) X 3 =======> 6x + 3y + 21z = 15

Eq (3) X 7 =======> 28x - 7y + 21z = 35

(-) (+) (-) (-)

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- 22x + 10y = - 20 --------------------> (4)

Multiply Eq (2) with 5 and add to Eq (4)

Eq (2) X 5 =======> 15x - 10y = - 5

Eq (4 ==========> - 22x + 10y = -20

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- 7x = - 25

7x = 25

x = 25/7

Substitute x = 25/7 in Eq (2)

3(25/7) - 2y = -1

75/7 - 2y = -1

75/7 + 1 = 2y

2y = (75 + 7)/7

2y = 82/7

y = 82/(7 X 2)

y = 41/7

Substitute x = 25/7 and y = 41/7 in Eq (1)

2(25/7) + 41/7 + 7z = 5

50/7 + 41/7 + 7z = 5

(50 + 41)/7 + 7z = 5

(91)/7 + 7z = 5

13 + 7z = 5

7z = 5 - 13

7z = - 8

z = - 8/7

Answer :

The Solutions are x = 25/7, y = 41/7 and z = -8/7.

answered Oct 29, 2018 by homeworkhelp Mentor

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