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18x - 9y + 3z = 18
First, just to clean it up a bit, divide both sides of the equation by 3.
(This doesn't change the equation or its graph in any way.)
6x - 3y + z = 6
At the 'x'-intercept, 'y' and 'z' are zero:
6x = 6
x = 1
At the 'y'-intercept, 'x' and 'z' are zero:
-3y = 6
-y = 2
y = -2
At the 'z'-intercept, 'x' and 'y' are zero:
z = 6
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