The standard form of a linear equation is: color(red)(A)x + color(blue)(B)y = color(green)(C)Ax+By=C
where, if at all possible, color(red)(A)A, color(blue)(B)B, and color(green)(C)Care integers, and A is non-negative, and, A, B, and C have no common factors other than 1
First, expand the terms in parenthesis:
y - 3 = (-2.4 xx x) + (2.4 xx 5)y−3=(−2.4×x)+(2.4×5)
y - 3 = -2.4x + 12y−3=−2.4x+12
Next, add color(red)(3)3 and color(blue)(2.4x)2.4x to each side of the equation to move towards the standard form while keeping the equation balanced:
color(blue)(2.4x) + y - 3 + color(red)(3) = color(blue)(2.4x) - 2.4x + 12 + color(red)(3)2.4x+y−3+3=2.4x−2.4x+12+3
2.4x + y - 0 = 0 + 152.4x+y−0=0+15
2.4x + y = 152.4x+y=15
Now, we multiply each side of the equation by color(red)(5)5 to convert all coefficients to integers while keeping the equation balanced:
color(red)(5)(2.4x + y) = color(red)(5) xx 155(2.4x+y)=5×15
(color(red)(5) xx 2.4x) + (color(red)(5) xx y) = 75(5×2.4x)+(5×y)=75
color(red)(12)x + color(blue)(5)y = color(green)(75)12x+5y=75
