Answer:
{x,y,z} = {-116,28,37}
Explanation:
// Solve equation [3] for the variable z
[3] 5z = -2x - 2y + 9
[3] z = -2x/5 - 2y/5 + 9/5
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// Plug this in for variable z in equation [1]
[1] 5x + 9y + 9•(-2x/5-2y/5+9/5) = 5
[1] 7x/5 + 27y/5 = -56/5
[1] 7x + 27y = -56
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// Plug this in for variable z in equation [2]
[2] 4x + 9y + 6•(-2x/5-2y/5+9/5) = 10
[2] 8x/5 + 33y/5 = -4/5
[2] 8x + 33y = -4
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// Solve equation [2] for the variable y
[2] 33y = -8x - 4
[2] y = -8x/33 - 4/33
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// Plug this in for variable y in equation [1]
[1] 7x + 27•(-8x/33-4/33) = -56
[1] 5x/11 = -580/11
[1] 5x = -580
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// Solve equation [1] for the variable x
[1] 5x = - 580
[1] x = - 116
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// By now we know this much :
x = -116
y = -8x/33-4/33
z = -2x/5-2y/5+9/5
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// Use the x value to solve for y
y = -(8/33)(-116)-4/33 = 28
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// Use the x and y values to solve for z
z = -(2/5)(-116)-(2/5)(28)+9/5 = 37
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