Question 1158969
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"The solution of the system of equations below is the set of all (x,y)such that 2x-3y=6. What is the value of k?
18x-27y=54
6x+ky=-2k 
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The first equation of the system
{{{18x-27y=54}}}
{{{2*3*3x-3*3*3y=2*3*3*3}}}
{{{2x-3y=6}}}---------the same equation refered in the descriptive part before your listing of the equations of the system.


Your equation using k shows a coefficent on x being 6.  The way to get the simplified equation to have this same coefficient is multiply 2x-3y=6 by 3.  This gives you:
{{{6x-9y=18}}}.


Compare the corresponding parts.
{{{system(6=6, -9=k, 18=-2k)}}}

This shows that {{{k=-9}}}.