SOLUTION: Find three solutions to the system of equations x+5y+3z=9 2x+9y+7z=5 thanks

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Question 462633: Find three solutions to the system of equations
x+5y+3z=9
2x+9y+7z=5
thanks
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
From the first equation, x = 9 - 5y - 3z.
Then by substitution, 2( 9 - 5y - 3z) + 9y +7z = 5
<==> 18 - 10y - 6z + 9y + 7z = 5, or
-y + z = -13, or y = z + 13.
==> x = 9 - 5(z + 13) - 3z = 9- 5z - 65 - 3z = -56 - 8z, or x = -8z - 56.
If z = 0, the solution is (-56, 13, 0)
If z = 1, the solution is (-64, 14, 1)
If z = -1, the solution is (-48, 12, -1).