If 4/3 X-2/3Y=2, what is the value of 16X/4Y?

2 Answers
Dwight
Feb 5, 2018

If I am reading the equation correctly (see below) it can be simplified to #6/Y+2# but not evaluated.

Explanation:

I hope the equation reads #(4X)/3 - (2Y)/3 = 2# (the second term is not clear). If so, we can multiply each term by 3, to get

#4X-2Y=6# and the denominators are removed.

Now, solve for X (or rather, 16X):

#4X=6+2Y#

Multiply through by 4:

#16X = 24+8Y#

Now, the numerator in the second expression can be replaced:

#(24+8Y)/(4Y)=(6+2Y)/Y#

or, #6/Y+2#

SCooke
Feb 5, 2018

It is an infinite range of values because the original expression is a line. In terms of the Y term, it is:
#2Y + 6/Y#
In terms of X it is:
#(16X)/(8X - 12)#
The line is #Y = 2X - 3#
It may also be simplified as an expression to #(4X)/Y#

Explanation:

First, rearrange the given equation to give you the ratio of #X/Y#, then apply the desired multiplier.
#4/3X - 2/3Y = 2# Multiply by 3:

#4X - 2Y = 6# ; #4X = 2Y + 6# Divide by 2:

#2X = Y + 3# and/or #Y = 2X - 3# or #X = Y/2 + 3/2# Substitute into the desired ratio.

#(16X)/(4Y)# #(16X)/(4(2X - 3)) = (16X)/(8X - 12)#

#(16X)/(4Y)# #(16(Y/2 + 3/2))/(4Y) = (8Y + 24)/(4Y)#

#2Y + 6/Y#

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