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
Because both of the coefficients and the constant are integers we can first subtract #color(red)(2x)# from each side of the equation to group the #x# and #y# variable on the left side of the equation while keeping the equation balanced:
#-color(red)(2x) + y = -color(red)(2x) + 2x - 3#
#-2x + y = 0 - 3#
#-2x + y = -3#
Now, we multiply each side of the equation by #color(red)(-1)# to convert the #x# coefficient to a positive coefficient while keeping the equation balanced:
#color(red)(-1)(-2x + y) = color(red)(-1) xx -3#
#(color(red)(-1) xx -2x) + (color(red)(-1) xx y) = 3#
#color(red)(2)x - color(blue)(1)y = color(green)(3)#
