Question 995177
.
{{{system(y=18x-9,
-108x+6y=-54)}}}.


Rewrite it in the standard form


{{{system(18x - y = -9,
-108x + 6y = -54)}}}.


The rows of coefficients are proportional with the proportionality coefficient  -6  (or  {{{-1/6}}}).  The right side terms are proportional with the same coefficient. 

Hence, &nbsp;the equations are &nbsp;<U>dependent</U>. &nbsp;The straight lines that correspond to these equations are parallel. &nbsp;Moreother, &nbsp;they have the common point &nbsp;(x,y) = &nbsp;(0,-9) 

and, &nbsp;therefore, coincide. &nbsp;Hence, &nbsp;the system is &nbsp;<U>consistent</U>.


See the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/coordinate/lessons/Geom-interpret-of-the-lin-system-of-two-eqns-with-two-unknowns.lesson>Geometric interpretation of the linear system of two equations in two unknowns</A>&nbsp; in this site.