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
To transform, first, multiply each term in parenthesis on the right side of the equation by #color(red)(1.4)#
#y + 2.1 = (color(red)(1.4) xx x) - (color(red)(1.4) xx 5)#
#y + 2.1 = 1.4x - 7#
Next, subtract #color(red)(2.1)# and #color(blue)(1.4x)# from each side of the equation:
#-color(blue)(1.4x) + y + 2.1 - color(red)(2.1) = -color(blue)(1.4x) + 1.4x - 7 - color(red)(2.1)#
#-1.4x + y + 0 = 0 - 9.1#
#-1.4x + y = -9.1#
Now, multiply each side of the equation by #color(red)(-10)# to complete the transformation:
#color(red)(-10)(-1.4x + y) = color(red)(-10) xx -9.1#
#(color(red)(-10) xx -1.4x) + (color(red)(-10) xx y) = 91#
#14x - 10y = 91#
