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it is a well known postulate that two lines always meet at only one point.there can not be more than one point where two lines can intersect.
\n" ); document.write( "Now consider the following system of linear equations
\n" ); document.write( " a*x+b*y=c ......(1)
\n" ); document.write( " g*x+f*y=d ........(2)
\n" ); document.write( " let they both intersect at two distinct points say (x1,y1) and (x2,y2)
\n" ); document.write( " then we will have
\n" ); document.write( " a*x1+b*y1=c a*x2+b*y2=c
\n" ); document.write( " g*x1+f*y1=d and g*x2+f*y2=d
\n" ); document.write( "so a*x1+b*y1=a*x2+b*y2 :::> a*(x1-x2)=b*(y2-y1)
\n" ); document.write( "similarly from others g*(x1-x2)=f*(y2-y1)
\n" ); document.write( "by dividing these equations we get a/g=b/f which can not be possible because lines are not parallel according to our supposition.hence
\n" ); document.write( " x1-x2=0 and y2-y1=0
\n" ); document.write( " x1=x2 and y1=y2
\n" ); document.write( "which prove that points are not distinct . \n" ); document.write( "