Can someone please explain the steps to solve the attached problem?  Thanks!

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The set of equations x + y + z = 2, 2x + 2y - 3z = 11 and 3x - y + z = 4 has to be solved.

x + y + z = 2

=> x = (2 - y - z)

Substitute in 2x + 2y - 3z = 11

=> 2*(2 - y - z) + 2y - 3z = 11

=> 4 - 2y - 2z + 2y - 3z = 11

=> 4 - 2z - 3z = 11

=> -5z = 7

=> z = -7/5

x + y + z = 2

=> x + y = 2 + 7/5

3x - y + z = 4

=> 3x - y = 4 + 7/5

4x = 6 + 14/5

=> x = 11/5

y = 2 + 7/5 - 11/5

=> y = 6/5

The solution of the system of equations is x = 11/5, y = 6/5 and z = -7/5

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