What is the value of y in the solution to the following system of equations #5x-3y=-112, x-6y=-14#?

To solve for an unknown you need to manipulate things so that you just 1 unknown

I chose to get rid of #x# as we need to have just the unknown of #y#

Given:

#5x-3y=-122" "..............................Equation(1)#
#color(white)(5)x-6y=-14" "...............................Equation(2)#
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Consider #Equation(2)#

Add #6y#to both sides giving:

#x=6y-14" "...............................Equation(3)#

Using equation(3) substitute for #x# in equation(1)

#color(green)(5color(red)(x)-3y=-122" "->" "5(color(red)(6y-14))-3y=-122#

#" "color(green)(30y-70-3y=-122)#

#" "color(green)(27y-70=-122)#

Add 70 to both sides
#" "color(green)(27y=-122+70#

#" "color(green)(27y=-52)#
Divide both sides by 27
#" "color(green)(y=-52/27)#