Equivalent means "equal to"
Because we are looking for an equation that is not equivalent to 3y + x = 18, we need to find one that is not equal to 3y + x = 18.
First, lets try y = 6 - 1/3x
3y + x = 18
Divide the whole of both sides by 3
y + 1/3x = 6
Then, subtract 1/3x from each side
y = 6 - 1/3x
So, y = 6 - 1/3x IS equivalent to 3y + x = 18, so it is not the answer.
Next, lets try y - 5 = -1/3 (x - 3)
First, we need to distribute the -1/3 in the right side.
y - 5 = -1/3x + 1
Add 5 to each side
y = -1/3x + 6
Add 1/3x to each side
y + 1/3x = 6
So, y + 1/3x = 6 is NOT equivalent to 3y + x = 18, so it IS an answer.
Lets try the third one: y - 5 = 1/3(x + 3)
We need to use distributive property again on the right side
y - 5 = 1/3x + 1
Add 5 to each side
y = 1/3x + 6 is not equivalent to 3y + x = 18 so it IS and answer
Lets test the last one: 6y + 2x = 36
Divide the whole of each side by 2
3y + x = 18 IS equivalent to 3y + x = 18 so it is NOT an answer
