Solve this system of equations. {12x+6y+7z= 35 {7x-5y-6z= 200 {x+y= -10

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The following system of equations has to be solved:

12x+6y+7z= 35 ...(1)

7x-5y-6z= 200 ...(2)

x+y= -10 ...(3)

From (3) x = -10 - y

Substitute in (1)

12(-10 - y) + 6y + 7z = 35

=> -120 - 12y + 6y + 7z = 35

=> 7z = 155 + 6y

=> z = (155 + 6y)/7

Substitute for x and z in (2)

7x-5y-6z= 200

=> 7(-10 - y) - 5y - 6*(155 + 6y)/7 = 200

=> 49(-10 - y) - 35y - 6(155 + 6y) = 1400

=> -490 - 49y - 35y - 930 - 36y = 1400

=> -120y = 2820

=> y = -47/2

x = 27/2

z = (155 + 6y)/7 = 2

The solution of the system of equations is x = 27/2, y = -47/2 and z = 2

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