Which of the following equations could be the result of using the comparison method to solve the system shown?

x - 4y - 1 = 0
x + 5y - 4 = 0

4y + 1 = 4 - 5y
-4y + 1 = 4 - 5y
4y + 1 = 5y - 4

Question

Which of the following equations could be the result of using the comparison method to solve the system shown?

x - 4y - 1 = 0
x + 5y - 4 = 0


4y + 1 = 4 - 5y
-4y + 1 = 4 - 5y
4y + 1 = 5y - 4

cherie_magee · Answer

@whpalmer4 can you help me with this

whpalmer4 · Answer

@cherie_magee do you understand the comparison method?

whpalmer4 · Answer

it's relying on the fact that the left sides of the two equations both equal the same value (0), so you take the two left sides and set them equal to each other

whpalmer4 · Answer

That means we can write
$$x-4y-1 = x+5y-4$$Subtract $x$ from both sides and we get
$$-4y -1 = 5y-4$$That doesn't match any of the answer choices above, but there's a little trick: multiply everything by -1 (changing the sign of everything) and you'll get an equation that does match one of the answers.  As we've multiplied everything in the equation by the same value, the equation remains true even though all of the coefficients are now different.