What is the solution of the set of equations 3x + 5y + z = 1, x - y + z = 8 and x + y - z = 6

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The following set of equations has to be solved for x, y and z.

3x + 5y + z = 1 ...(1)

x - y + z = 8 ...(2)

x + y - z = 6 ...(3)

Add (2) and (3)

x - y + z + x + y - z = 8 + 6

=> 2x = 14

=> x = 7

Substitute x = 7 in (1)

21 + 5y + z = 1

=> 5y + z = -20

=> z = -20 - 5y

Substitute z = -20 - 5y and x = 7 in (2)

7 - y - 20 - 5y = 8

=> -6y = 21

=> y = -7/2

z = -20 - 5*(-7/2) = -5/2

The solution of the set of equations is x = 7, y = -7/2 and z = -5/2

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