Question

Given the equations x = 6y, 4y = 9z, and (3x)(9z) = ky, what is the value of k in terms of y, if y ≠ 0?

Answer 1

So, this question is a substitution equation, and the end goal, from my experience would be to try and get all of the equations into one place, with as few variables as possible. Can you see where to begin?

Answer 2

multiply by 3?

Answer 3

Sort of; notice, first, how 9z appears in the last two equations? By replacing 9z with the 4y it equals in the last equation, you eliminate a variable from the one equation containing a k. Remember, your end goal is to find out k in relation to y.

Answer 4

but why do i need the first two equations if there isn't a k in them

Answer 5

To replace the 3x and 9z in the last equation. Instead of having 3x(9z)=ky, by substituting, the equation becomes 72y=ky, which can be further simplified into the answer.

Answer 6

Do you see how I got that?

Answer 7

by multiplying 3 by 9 and flipping it? jk.

Answer 8

Because of the equation 9z=4y, which is a given statment and thus true, we can substitute 4y into the last equation, and eliminate 9z from it, thus being able to make the final equation a ky problem, as opposed to a kyxz problem. X and z are distractors.

Answer 9

To finish off, divide the left side of the equation by y, so that 72=k is your solution.

Answer 10

Does that make sense?

Answer 11

Refer to the Mathematica attachment.