Question 1158969
{{{18x-27y=54}}}
{{{6x+ky=-2k}}}.......both sides multiply by {{{3}}}
---------------------
{{{18x-27y=54}}}
{{{18x+3ky=-6k}}}
--------------------------subtract

{{{18x-27y-18x-3ky=54-(-6k)}}}

{{{-27y-3ky=54+6k}}}........group

{{{(-3ky-27y)=(6k+54)}}}...factor out common

{{{-3y(k + 9) = 6(k + 9)}}}

{{{-3y(k + 9)- 6(k + 9)=0}}}

{{{(-3y - 6 )(k + 9)=0}}}

=>
{{{(k + 9)=0}}} -> {{{highlight(k=-9)}}}

{{{-3y- 6 =0}}}=>{{{3y=-6}}}->{{{y=-2}}}

find {{{x}}}

{{{6x-9(-2)=-2(-9)}}}

{{{6x+18=18}}}

{{{6x=18-18}}}

{{{6x=0}}}

{{{x=0}}}

so, check your system:

{{{18x-27y=54}}}
{{{18*0-27(-2)=54}}}
{{{54=54}}}-> true

{{{6x+ky=-2k}}}
{{{6*0-9(-2)=-2(-9)}}}
{{{18=18}}}->true