#c-d=8# and #c/5=d+4#
Let's start with #c/5=d+4#
Multiply both sides by #color(red)5# to get rid of the fraction.
#color(red) 5 * c/5 = color(red)5 * (d+4)#
#color(blue)c=5d+20#
Now substitute for #color(blue)c# in #color(blue)c-d=8#
#color(blue)(5d+20)-d=8#
Combine like terms.
#4d+20=color(white)(a)8#
#color(white)(aa)-20color(white)a-20color(white)(aaa)#Subtract 20 from both sides
#4d=-12#
#(4d)/4=-12/4color(white)(aaa)#Divide both sides by 4
#d=-3#
To solve for #c#, plug #color(limegreen)d =color(limegreen)(-3)# into the original equation #c-color(limegreen)d=8#
#c-(color(limegreen)(-3))=8#
#c+3=color(white)a8#
#color(white)(a)-3color(white)(a)-3color(white)(aaa)#Subtract 3 from both sides
#c=5#
