Math Help - Simultaneous Equations (LAME theory).

1. Simultaneous Equations (LAME theory).

Hi,

I have come to a standstill while trying to follow an example. I have attached the full example but need some assistance in the method used to solve the simultaneous equations where b=510kN & a=104MPa.

If anyone could break down the steps involved in solving the simultaneous equations it would be much appreciated...

Many thanks in advance. I hope my question is clear....

2. Re: Simultaneous Equations (LAME thorey) Help!

You know that $-100\times 10^6= a- b/.05^2$ and $0= a- b/.07^2$ so you have two linear equations to solve for a and b. One obvious thing to do (assuming you really mean " $a- \frac{b}{0.05^2}$" and not " $\frac{a- b}{0.05^2}$") is to subtract the second equation from the first, eliminating a: $-100\times 10^6- 0= \left(a- \frac{b}{0.0004}\right)- \left(a- \frac{b}{0.0049}\right)= \frac{b}{0.0049}- \frac{b}{0.0004}$.

Get common denominators to combine the fractions, then solve for b. Once you know b, solve either of the original two equations for a. Once you know a, b, and r, you can just do the arithmetic to find $\sigma_c= a+ b/r^2$

3. Re: Simultaneous Equations (LAME thorey) Help!

Thanks for the help, problem solved!