Question

Is y=6x+9 27x-3y=-81 parallel

Answer 1

The answer is:  "No;  they are not parallel."
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Explanation:
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Given:

y = 6x + 9 ;  AND

27x - 3y = -81 ;
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We need to rewrite:  
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" 27x - 3y = -81" ; in "slope-intercept form"; that is:  
                                       " y = mx + b" ; and see if the "slope, "m" ;  is the same                                                    as:  "y = 6x + 9" ;  or "6";
 (that is, whether "m = 6";  when an equation is written is "slope-intercept form",  the slope, "m", is the coefficient of "x";  and we are given an equation that is already written in:  "slope-intercept form":
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" y = 6x + 9 " ;  in which, the slope, "m", = "6".
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If  we can write the other equation given:
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" 27x - 3y = -81 " ; in "slope-intercept form"; and "m = 6"; (the same slope), then both equations are "parallel" to each other.
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Given:
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 27x - 3y = -81 ; 
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 Let us write this in "slope-intercept form" ;
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Let us multiply the ENTIRE equation (both sides) by "-1"; to get rid of most of the 'negatives' :
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 -1* {27x - 3y = -81} ; 
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 to get:  
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     -27x + 3y = 81 ;
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Now, add "27x" to EACH SIDE of the equation:
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        -27x + 3y + 27x = 81 + 27x ;
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 to get:  3y = 81 + 27x ;  ↔  3y = 27x + 81; 
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Now, divide the ENTIRE EQUATION (both sides) by "3"; to isolate "y" on the left-hand side of the equation; and to re-write the equation in "slope-intercept form:
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     3y / 3 = (27x + 81) / 3 ;
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              y = 9x + 27 ;
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   So, y = mx + b ;  m = "9"; which is not "6" ; 
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So the answer is:  "No; they are not parallel."
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Answer 2

No.  The equations can be solved for x and y and so they are not parallel.
x = -6  y= -27