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

Question

Hazel Anglin · Accepted Answer

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

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#

Eli Assouline · Answer

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# 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#