1. The second step is to solve these independent equations one by one. 2. This is done by means of the following independent equations : 3. These are 6 independent equations relating stresses and strains. 4. Alternatively, the solution can be found by jointly solving any two independent equations . 5. These are 6 independent equations relating strains and displacements with 9 independent unknowns ( strains and displacements ). 6. Equivalently, if a system has more independent equations than unknowns, it is inconsistent and has no solutions. 7. Although there appear to be 64 equations in Faraday-Gauss, it actually reduces to just four independent equations . 8. Four unknowns cannot be found given two independent equations in these unknown variables and hence the beam is statically indeterminate. 9. In keeping with the idea that they usually represent time, their special significance vanishes in the time-independent equation . 10. The number of independent equations in the original system is the number of non-zero rows in the echelon form.
