Given:

#+3x-8y=-7" ".........................Equation(1)#

#-5x-6y=3" ".............................Equation(2)#

Consider #Eqn(1)#

Add #8y# to both sides

#3x=8y-7#

Divide both sides by 3

#color(red)(x=8/3y-7/3)" "...........................Equation(1_a)#

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Using #Eqn(1_a)# substitute for #x# in #Eqn(2)#

#color(green)(-5(color(red)(x))-6y=3 color(white)("ddd")->color(white)("ddd")-5(color(red)((8y)/3-7/3))-6y=3 )#

#color(green)(color(white)("ddddddddddddddd")->color(white)("ddd")-(40y)/3+35/3color(white)("dd")-6y=3 )#

Put everything over 3 to make calculation more straight forward.

#color(green)(color(white)("ddddddddddddddd")->color(white)("ddd")-(40y)/3+35/3color(white)("dd")-(18y)/3=9/3 )#

Multiply both sides by 3

#color(green)(color(white)("ddddddddddddddd")->color(white)("ddd")-40y+35color(white)("dd")-18y=9#

#-58y=-26#

#y=+13/29#

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I will let you finish off