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 first add color(red)(14) to each side of the equation to have the constant on the right side of the equation while keeping the equation balanced:
2x - 4y - 14 + color(red)(14) = 0 + color(red)(14)
2x - 4y - 0 = 14
2x - 4y = 14
We can now divide each side of the equation by color(red)(2) to eliminate a common factor of each term while keeping the equation balanced:
(2x - 4y)/color(red)(2) = 14/color(red)(2)
(2x)/color(red)(2) - (4y)/color(red)(2) = 7
x - 2y = 7
color(red)(1)x - color(blue)(2)y = color(green)(7)
