Question 224275
To  remove  fractions  multiply  1st  eqn  by  4  and  2nd  by 3
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(1)  3x +1y =6
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(2) -3x -1y =-6,,,,,,,,,,now  multiply  (2)  by (-1)
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(2a) 3x +1y =6,,,,,,,,,,this  shows  that  (1)  is  the  same  as (2a),,,or  coincident,  and  the  lines  overlap,,  and  there  are  infinite  solutions (infinite  coordinates  that  satisfy  either  line)
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When  we  have  coincident  lines ,  we  do  get  a  true  statement,  without  variables,  which  means  that  any  variable(x) will  work,  with  the  correct  corresponding  variable (y) of  course.
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Therefore,  your  0=0  was  correct.  and  the  answer  is  as  stated  above.