How do you write #4y-5x=3(4x-2y+1)# in standard form?

Question

Avery Alexander · Accepted Answer

See the entire solution process below:

First, expand the terms in parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis: #4y - 5x = color(red)(3)(4x - 2y + 1)# #4y - 5x = (color(red)(3) * 4x) - (color(red)(3) * 2y) + (color(red)(3) * 1)# #4y - 5x = 12x - 6y + 3# 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. To convert to the Standard Form of a linear equation we need to first subtract #color(red)(12x)# and add #color(blue)(6y)# to each side of the equation to get the #x# and #y# terms on left side of the equation while keeping the equation balanced: #-color(red)(12x) + color(blue)(6y) + 4y - 5x = -color(red)(12x) + color(blue)(6y) + 12x - 6y + 3# #-color(red)(12x) - 5x + color(blue)(6y) + 4y = -color(red)(12x) + 12x + color(blue)(6y) - 6y + 3# #(-color(red)(12) - 5)x + (color(blue)(6) + 4)y = 0 - 0 + 3# #-17x + 10y = 3# Now, multiply each side of the equation by #color(red)(-1)# to ensure the coefficient of the #x# is a positive integer: #color(red)(-1)(-17x + 10y) = color(red)(-1) * 3# #(color(red)(-1) * -17x) + (color(red)(-1) * 10y) = -3# #17x + (-10y) = -3# #color(red)(17)x - color(blue)(10)y = color(green)(-3)#

Eva Adamson · Answer

undefined To write the equation $4y - 5x = 3(4x - 2y + 1)$ in standard form, expand and rearrange the terms to have the form $Ax + By = C$. This results in $23x + 10y = 3$.