Given:
#-x+3y=-9" "......................Equation(1)#
#color(white)("d")8x-4y=32" ".........................Equation(2)#
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#color(blue)("Determine the value of "y" - in detail using first principles")#
#color(brown)("Consider "Eqn(1))#
#color(brown)("Multiply both sides by "(-1))#
#+x-3y=+9#
#color(brown)("Add "3y" to both sides")#
#x=9+3y" ".......Equation(1_a)#
#color(brown)("Using "Eqn(1_a)" substitute for "x" in "Eqn(2))#
#color(green)(8color(red)(x)-4y=32 color(white)("dddd")->color(white)("dddd")8(color(red)(9+3y))-4y=32 )#
#color(green)( color(white)("dddddddddddddd.")->color(white)("dddd")72+24y-4y=32 )#
#color(green)( color(white)("dddddddddddddd.")->color(white)("dddd")72+20ycolor(white)("dddd")=32 )#
#color(brown)("Subtract 72 from both sides")#
#color(green)( color(white)("dddddddddddddd.")->color(white)("dddddddd")20ycolor(white)("dddd")=-40 )#
#color(brown)("Divide both sides by 20")#
#color(green)( color(white)("dddddddddddddddd.")->color(white)("dddddddd")ycolor(white)("dddd")=-2 )#
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#color(blue)("Determine the value of "x" - not so much detail")#
#color(brown)("Substitute for "y" in "Eqn(1))#
#-x+3y=-9color(white)("dddd")->color(white)("dddd")-x+3(-2)=-9#
#color(white)("ddddddddddddddddddddddddd")->color(white)("dddd") -x=-3#
#x=3#
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#color(blue)("Check")#
#-x+3y color(white)("d")->color(white)("d")-3+(3xx-2) ->9 # as required
#8x-4y color(white)("d")->color(white)("d") 8(3)-4(-2) -> 24+8->32# as req'd