Solve the following equations: 2x – y + z = –3 2x + 2y + 3z = 2 3x – 3y – z = –4

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We have to solve the following set of equations:

2x – y + z = –3...(1)

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

3x – 3y – z = –4 ...(3)

(2) - (1)

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

=> 3y + 2z = 5 ...(4)

2*(3) - 3*(2)

=> 6x - 6y - 2z - 6x - 6y - 9z = -8 - 6

=> -12y - 11z = -14

=> 12y + 11z = 14 ...(5)

(5) - 4*(4)

=> 12y + 11z  - 12y - 8z = 14 - 20

=> 3z = -6

=> z = -2

Substitute in (4)

3y + 2*(-2) = 5

=> 3y = 5 + 4

=> y = 3

Substitute z and y in (1)

2x – y + z = –3

2x - 3 - 2 = -3

=> 2x = 2

x = 1

The required values are x = 1 , y = 3 and z = -2

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