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Determine if the ordered triple (2,4,3) is a solution of the system. 5x + y + z = 17 x - y + 2z = 4 x + y +...

Determine if the ordered triple (2,4,3) is a solution of the system.
5x + y + z = 17
x - y + 2z = 4
x + y + z = 9
solution
not a solution

Answer

To determine if the ordered triple (2,4,3) is a solution, substitute x = 2, y = 4, z = 3 into each equation:

5x + y + z = 17: 5(2) + 4 + 3 = 10 + 4 + 3 = 17. This equation is satisfied.
x - y + 2z = 4: 2 - 4 + 2(3) = 2 - 4 + 6 = 4. This equation is satisfied.
x + y + z = 9: 2 + 4 + 3 = 9. This equation is satisfied.

Since the ordered triple satisfies all equations, it is a solution.

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