Question

solve this equation x+2y+2z=6, -2x+4y+6z=-3, x+3y+z=6

Answer 1

x + 2y + 2z = 6 -->(-1)
x + 3y + z = 6
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-x - 2y - 2z = -6 (result of multiplying by -1)
x + 3y + z = 6
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y - z = 0

x + 2y + 2z = 6 -->(2)
-2x + 4y + 6z = -3
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2x + 4y + 4z = 12 (result of multiplying by 2)
-2x + 4y + 6z = -3
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8y + 10z = 9

y - z = 0 --->(-8)
8y + 10z = 9
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-8y + 8z = 0 (result of multiplying by -8)
8y + 10z = 9
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18z = 9
z = 1/2

y - z = 0
y - 1/2 = 0
y = 1/2

x + 2y + 2z = 6
x + 2(1/2) + 2(1/2) = 6
x + 1 + 1 = 6
x + 2 = 6
x = 6 - 2
x = 4

check..
x + 3y + z = 6
4 + 3(1/2) + 1/2 = 6
4 + 3/2 + 1/2 = 6
4 + 4/2 = 6
4 + 2 = 6
6 = 6 (correct)

x = 4, y = 1/2 and z = 1/2