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)(0.2y)# from each side of the equation so the #x# and #y# terms are on the left side of the equation as required by the Standard Form while keeping the equation balanced:
#0.25x - color(red)(0.2y) = 0.1 + 0.2y - color(red)(0.2y)#
#0.25x - 0.2y = 0.1 + 0#
#0.25x - 0.2y = 0.1#
Next, multiply each side of the equation by #color(red)(20)# to eliminate the decimals and to make all of the coefficients integers while keeping the equation balanced:
#color(red)(20)(0.25x - 0.2y) = color(red)(20) xx 0.1#
#(color(red)(20) xx 0.25x) - (color(red)(20) xx 0.2y) = 2#
#color(red)(5)x - color(blue)(4)y = color(green)(2)#
#A = color(red)(5)#
#B = color(blue)(4)#
#C = color(green)(2)#
