Use linear regression to make an inverse prediction

I have a problem I am trying to solve using the R programming language and software environment. This isn't a programming question but more how I can use the results however I might describe the problem is more programming speak rather than mathematical.

I have a set of observed data where I have variables V1..V11. V11 is an individuals weight and V1..V10 are all factors which impact the weight. I have performed regression on this data like so.

lm(formula = V11 ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10, data = fDF)


This gives me the results

Coefficients:
(Intercept)           V1           V2           V3           V4           V5
58.8082       2.4857       0.5811       0.8833       2.8648       7.7457
V6           V7           V8           V9          V10
-7.3599       3.2055      -6.6382       1.4559       0.8486


Is it possible using these coefficients solve the inverse of this problem. So given the weight V11 can you predict the values of v1..v10?

@MichaelChernick : Even in the simple regression you speak of, there's not enough information given in the posting. If you knew the number of data points and the correlation you could do it. With the information in the anova table, plus a bit of algebra, you could do it. But if the predicted value of $y$ given $x$ is $y=mx+b$, then inverse of that function, $x = (y-b)/m$, is NOT the function you'd use, and not enough information is given to find the right one. –  Michael Hardy Aug 9 '12 at 18:54