#:.1/9x-3/13y=1#----(1)
#:.3/2x-8y=2#----(2)
multiply # (2) xx 2#
#:.3x-16y=4#
#:.-16y=-3x+4#
#:.16y=3x-4#
#:.color(blue)(y=(3x-4)/16#
substitute #color(blue)(y=(3x-4)/16#--- in # (2)#
#:.3/2x-8((3x-4)/16)=2#
#:.3/2x-(24x+32)/16=2#
multiply both sides by 16
#:.24x-24x+32=32#
#:.24x-24x=32-32#
#:.0=0#
#:.color(blue)(x=0#
substitute #color(blue)(x=0# in #(2)#
#:.3/2(color(blue)0)-8y=2#
#:.-8y=2#
multiply both sides by# -1#
#:.8y=-2#
#:.y=-2/8#
#:.color(blue)(y=-0.25# or #color(blue)( -1/4#
check:
substitute #color(blue)(y=-0.25# in #(2)#
#:.3/2x-8(color(blue)(-0.25))=2#
#:.3/2x+2=2#
#:.3/2x=2-2#
#:.3/2x=0#
#:.color(blue)(x=0#
