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
Because both of the coefficients and the constant are integers we can first subtract color(red)(2x) from each side of the equation to group the x and y variable on the left side of the equation while keeping the equation balanced:
-color(red)(2x) + y = -color(red)(2x) + 2x - 3
-2x + y = 0 - 3
-2x + y = -3
Now, we multiply each side of the equation by color(red)(-1) to convert the x coefficient to a positive coefficient while keeping the equation balanced:
color(red)(-1)(-2x + y) = color(red)(-1) xx -3
(color(red)(-1) xx -2x) + (color(red)(-1) xx y) = 3
color(red)(2)x - color(blue)(1)y = color(green)(3)
