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, we need to move the #x# term to the left side of the equation by subtracting #color(red)(2x)# from each side of the equation:
#-color(red)(2x) + y = -color(red)(2x) + 2x - 5#
#-2x + y = 0 - 5#
#-2x + y = -5#
Another requirement is for the #x# coefficient to be non-negative. Therefore, we must multiply each side of the equation by #color(red)(-1)#:
#color(red)(-1)(-2x + y) = color(red)(-1) * -5#
#(color(red)(-1) * -2x) + (color(red)(-1) * y) = 5#
#2x - y = 5#
#color(red)(2)x - color(blue)(1)y = color(green)(5)#
