"standard form" for a linear equation is
#color(white)("XXX")color(red)Ax+color(blue)By=color(magenta)C#
where
#color(white)("XXX")color(red)A, color(blue)B, color(magenta)C # are integers
#color(white)("XXX")#(and usually with the restriction that #color(red)A>=0#)
Given
#color(white)("XXX")1/2x+1/2y=6#
Multiplying everything by #2# converts the coefficients to integers:
#color(white)("XXX")color(red)1x+color(blue)1y=color(magenta)(12)#
Relating this back to the "standard form" we have
#color(white)("XXX")color(red)A=color(red)1#
#color(white)("XXX")color(blue)B=color(blue)1# and
#color(white)("XXX")color(magenta)C=color(magenta)(12)#
