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)(3x) from each side of the equation so both the x and y terms are on the left side of the equation as required by the Standard form while keeping the equation balanced.
-color(red)(3x) + y = -color(red)(3x) + 3x - 5
-3x + y = 0 - 5
-3x + y = -5
Now, multiply each side of the equation by color(red)(-1) to make the x coefficient non-negative as required by the Standard form while keeping the equation balanced.
color(red)(-1)(-3x + y) = color(red)(-1) * -5
(color(red)(-1) * -3x) + (color(red)(-1) * y) = 5
color(red)(3)x + color(blue)(-1)y = color(green)(5)
Or
color(red)(3)x - color(blue)(1)y = color(green)(5)
color(red)(A = 3)
color(blue)(B = -1)
color(green)(C = 5)
