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)(11)# from each side of the equation to isolate the #x# and #y# terms on the left side of the equation and the constant on the right side of the equation while keeping the equation balanced:
#-7y - 10x + 11 - color(red)(11) = 0 - color(red)(11)#
#-7y - 10x + 0 = -11#
#-7y - 10x = -11#
Next, rearrange the terms on the left side of the equation so the #x# term is first:
#-10x - 7y = -11#
Now, multiply each side of the equation by #color(red)(-1)# so the coefficient of the #x# term is non-negative while keeping the equation balanced:
#color(red)(-1)(-10x - 7y) = color(red)(-1) xx -11#
#(color(red)(-1) xx -10x) + (color(red)(-1) xx -7y) = 11#
#color(red)(10)x + color(blue)(7)y = color(green)(11)#
