Expert: Scott A Wilson - 11/28/2009

Question
Hi pls. i need ur help for the following:

- find the value of y?
y= 4x - 2, x=8

- find the value of y?
2y-1     y+3
----- -  ---- = y-2
 3       2  

Answer
If x=8 and y=x-2, put in 8 for x into the second equation.
The answer is y = 4(8) - 2 = 32-2 = 30.

For the next one, it would translate better if it were written as (2y-1)/3 - (y+3)/2 = y-2.

To make it easier to look at, eliminate the fractions.
Since there is a 2 and a 3 in the denominator, multiply by both 2 and 3 and get 6.

So multiply by 6 and gete 6(2y-1)/3 - 6(y+3)/2 = 6(y-2).
In the 1st fraction, 6/3=2, so we have 2(2y-1), which works out to be 4y-2.
In the 2nd fraction, -6/2=-3, so we have -3(y+3), which works out to be -3y-9.
On the right side we have 6(y-2), which turns into 6y-12.

We can then rewrite the equation 4y-2  -3y-9 = 6y-12.
Now on the left side, 4y-3y=y and -2-9=-11, so we have y - 11 = 6y - 12.
Adding -6y to both sides gives -5y - 11 = -12.
Adding 11 to both sides gives -5y = -1.
Dividing by -5 gives y = 1/5.

Checking that against the original equation gives (2/5 - 1)/3 - (1/5 + 3)/2 = 1/5 - 2.
Now 2/5 - 1 = 2/5 - 5/5 = -3/5, and over 3 makes it -1/5.
Next, -(1/5 + 3) is -(1/5 + 15/5) = -16/5, and when we divide this by 2 we get -8/5.
On the right side, 1/5 - 2 = 1/5 - 10/5 = -9/5.
So when we put it all back together, we get -1/5 - 8/5 = -9/5, and that is right,
so the answer is verified.