This is one of two approaches:
Given:
#2x-5y=-4" "..........Equation(1)#
# color(white)("d") x+6y=+4" "..........Equation(2)#
Multiply both sides of #Eqn(2)# by 2
#2x-color(white)("d")5y=-4" ".........Equation(1)#
#ul(2x+12y=+8" ".........Equation(2_a)larr" Subtract" )#
#color(white)("d")0-17y=-12#
By choosing negative it will change the #y# term into positive.
Divide both sides by #(-17)#
#color(blue)(color(white)("ddddddddddd")ul(bar(| color(white)(..) y=12/17color(white)(..)|)))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute for #color(red)(y=12/17)# into #Eqn(2)#
#color(green)(x+6color(red)(y)=4 color(white)("dddd")->color(white)("dddd")x+(6color(red)(xx12/17))=4 )#
#color(white)("ddddddddddddd")->color(white)("dddd")x+color(white)("ddd")72/17color(white)("d.d")=4#
#color(blue)(color(white)("ddddddddddd")ul(bar(| color(white)(..) x=-4/17color(white)(..)|)))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Check")#
#2x-5y=-4" "..........Equation(1)#
#color(white)("d")x+6y=+4" "..........Equation(2)#
#2(-4/17)-5(12/17)=-4" "..........Equation(1)#
#color(white)("d")(-4/17)+6(12/17)=+4" "..........Equation(2)#
#-8/17-60/17=-4" "..........Equation(1)#
#-4/17+72/17=+4" "..........Equation(2)#
#-4=-4" "..........Equation(1)#
#+4=+4" "..........Equation(2)#
