Step 1) Solve the second equation for #x#:
#3x = 5/4y + 2#
#color(red)(1/3) xx 3x = color(red)(1/3)(5/4y + 2)#
#color(red)(1/color(black)(cancel(color(red)(3)))) xx color(red)(cancel(color(black)(3)))x = (color(red)(1/3) xx 5/4y) + (color(red)(1/3) xx 2)#
#x = 5/12y + 2/3#
Step 2) Substitute #5/12y + 2/3# for #x# in the first equation and solve for #y#:
#12x - 5y = 8# becomes:
#12(5/12y + 2/3) - 5y = 8#
#(12 xx 5/12y) + (12 xx 2/3) - 5y = 8#
#(color(red)(cancel(color(black)(12))) xx 5/color(red)(cancel(color(black)(12)))y) + (color(red)(cancel(color(black)(12)))4 xx 2/color(red)(cancel(color(black)(3)))) - 5y = 8#
#5y + 8 - 5y = 8#
#5y - 5y + 8 = 8#
#0 + 8 = 8#
#8 = 8#
Because #8# does in fact equal #8# these two equations are parallel and the same. They have an infinite number of points the same.
