The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#
Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
First, subtract #color(red)(3x)# from each side of the equation so both the #x# and #y# terms are on the left side of the equation as required by the Standard form while keeping the equation balanced.
#-color(red)(3x) + y = -color(red)(3x) + 3x - 5#
#-3x + y = 0 - 5#
#-3x + y = -5#
Now, multiply each side of the equation by #color(red)(-1)# to make the #x# coefficient non-negative as required by the Standard form while keeping the equation balanced.
#color(red)(-1)(-3x + y) = color(red)(-1) * -5#
#(color(red)(-1) * -3x) + (color(red)(-1) * y) = 5#
#color(red)(3)x + color(blue)(-1)y = color(green)(5)#
Or
#color(red)(3)x - color(blue)(1)y = color(green)(5)#
#color(red)(A = 3)#
#color(blue)(B = -1)#
#color(green)(C = 5)#
