Solve the following system of equations: x + 3y + 2z = 1 2x + 5y + 11z = 21 x + 2y + 4z = 7

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The following system of equations has to be solved.

x + 3y + 2z = 1 ...(1)

2x + 5y + 11z = 21 ...(2)

x + 2y + 4z = 7...(3)

From (1)

x = 1 - 3y - 2z

(1) - (3)

=> y - 2z = -6

...

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The following system of equations has to be solved.

x + 3y + 2z = 1 ...(1)

2x + 5y + 11z = 21 ...(2)

x + 2y + 4z = 7...(3)

From (1)

x = 1 - 3y - 2z

(1) - (3)

=> y - 2z = -6

=> y = 2z - 6

Substitute in (2)

2x + 5y + 11z = 21

=> 2(1 - 3y - 2z) + 5(2z - 6) + 11z = 21

=> 2(1 - 3(2z - 6) - 2z) + 5(2z - 6) + 11z = 21

=> 2 - 6(2z - 6) - 4z + 10z - 30 + 11z = 21

=> 2 - 12z + 36 - 4z + 10z - 30 + 11z = 21

=> 5z = 13

=> z = 2.6

y = 2z - 6

=> -0.8

x = 1 - 3y - 2z

= 1 + 2.4 - 5.2

=> -1.8

The solution of the system of equations is x = -1.8, y = -0.8 and z = 2.6

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