If we multiply #-x+7y=3# by #4# it leads to
#-4x+28y=12#, the same as the second equation.
Hence #-x+7y=3# and #-4x+28y=12# represent same line
or two coinciding lines.
Now as #-x+7y=3# leads to #x=7y-3#, any point #(7k-3,k)# falls on these lines and hence the sets of equation has infinite solutions as putting any value of #k# will give a solution to 'two' equations.
Elimination method
Trying elimination method we have obtained #x=7y-3# from first equation and putting this in second eliminates #x# and we get
#-4(7y-3)+28y=12#
or #-4xx7y-4xx(-3)+28y=12#
or #-28y+12+28y=12#
or #12=12#
When we have such pair of equations, as may be observed, we find that other variable too is eliminated and we get #a=a#, where #a# is a real number (here #a=12#). This denotes 'two' coinciding lines (when graphed) and infinite solutions.
Note - if we get two unequal numbers #a=b#, where #a# and #b# are two different numbers, this means two parallel lines. For example one can try for #-x+7y=8# and #-4x+28y=12#.
