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)(0.2y) from each side of the equation so the x and y terms are on the left side of the equation as required by the Standard Form while keeping the equation balanced:
0.25x - color(red)(0.2y) = 0.1 + 0.2y - color(red)(0.2y)
0.25x - 0.2y = 0.1 + 0
0.25x - 0.2y = 0.1
Next, multiply each side of the equation by color(red)(20) to eliminate the decimals and to make all of the coefficients integers while keeping the equation balanced:
color(red)(20)(0.25x - 0.2y) = color(red)(20) xx 0.1
(color(red)(20) xx 0.25x) - (color(red)(20) xx 0.2y) = 2
color(red)(5)x - color(blue)(4)y = color(green)(2)
A = color(red)(5)
B = color(blue)(4)
C = color(green)(2)
