Given:
#2x-5y=9..................................(1)#
#5x-3y=2..................................(2)#
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#color(blue)("Consider Equation (1)")#
Add #5y# to both sides
#2x=9+5y#
Subtract 9 from both sides.
#2x-9 =5y#
Divide both sides by 5
#2/5 x-9/5 =y#
Write in conventional form
#color(green)(y=2/5x-9/5....................................(1_a))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider Equation (2)")#
Add #3y# to both sides
#5x=2+3y#
Subtract 2 from both sides
#5x-2=3y#
Divide both sides by 3
#5/3 x-2/3 = y#
Write in conventional form
#color(green)(y=5/3x-2/3....................................(2_a))#
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To end up with just 1 variable thus solvable.
#color(green)("Equation "(2_a))color(red)( =y= )color(blue)("Equation "(1_a)")#
#color(green)(2/5x-9/5) color(red)(=) color(blue)(5/3x-2/3)#
Collecting like terms
#2/5x -5/3x =9/5 -2/3#
#(6 -25)/15 x = (27 -10)/15#
#-19/15 x =17/15#
#-19x=17#
#color(red)(x=-17/19...........................(3))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute for #x# in Equation (1)
#2x-5y=9..................................(1)#
#2color(red)((-17/19)) -5y=9#
#5y= 2(-17/19) -9#
#y= 2/5(-17/19)-9/5#
#color(red)(y=-2 3/19=-41/19...............(4))#
