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, we need to move the x term to the left side of the equation by subtracting color(red)(2x) from each side of the equation:
-color(red)(2x) + y = -color(red)(2x) + 2x - 5
-2x + y = 0 - 5
-2x + y = -5
Another requirement is for the x coefficient to be non-negative. Therefore, we must multiply each side of the equation by color(red)(-1):
color(red)(-1)(-2x + y) = color(red)(-1) * -5
(color(red)(-1) * -2x) + (color(red)(-1) * y) = 5
2x - y = 5
color(red)(2)x - color(blue)(1)y = color(green)(5)
