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
We can multiply each side of the equation by #color(red)(30)# to eliminate the fractions and ensure the coefficients are integers while keeping the equation balanced:
#color(red)(30)(5/6x + 1/10y) = color(red)(30) xx 3/10#
#(color(red)(30) xx 5/6x) + (color(red)(30) xx 1/10y) = 90/10#
#(150x)/6 + (30y)/10 = 9#
#color(red)(25)x + color(blue)(3)y = color(green)(9)#
#color(red)(A = 25)#
#color(blue)(B = 3)#
#color(green)(C = 9)#
