Question

1). If a system is being carefully analyzed and it is found that three equations are obtained but there are 4 unknowns:

a: then numerical values should be immediately inserted into the equations to check for mistakes

b: the analysis should probably continue - for some systems a cancellation will eliminate one of the unknowns, and particularly if one of the unknowns is the mass of an object

c: the analysis should be ended and the expressions obtained handed in as the final answer

d: then we can be sure that the kinematic equation x=x0+v0t also applies

2) If the analysis of a system results in 3 or more equations in 3 or more unknowns:

a: the numerical values should be inserted into the expressions immediately to avoid making mistakes

b: the solutions will only be required in advanced physics classes for physics majors so is not of concern for this course

c: the solution will not be possible - the instructor should be notified

d: the analysis can typically be handled by progressing through the equations, eliminating the number of equations and unknowns one step at a time

Answer 1

1). If a system is being carefully analyzed and it is found that three equations are obtained but there are 4 unknowns:

If you have more unknowns than the number of equations, then you are probably going to have infinte number of solutions. For a homogenous system, if the number of unknowns exceeds the number of equations, then there will be infinite possible solutions with not all unkowns are equal to zero. Using reduced row echelon method, one can simplify or solve such system of equations.

a: then numerical values should be immediately inserted into the equations to check for mistakes

if the equations are homogenous and trivial, may be plugging in the numerical values help.

b: the analysis should probably continue - for some systems a cancellation will eliminate one of the unknowns, and particularly if one of the unknowns is the mass of an object

For a more clear answer, more specific informations are needed, such as the nature of the equations, homegeneous or non-homogenous, trivial or non-trivial.

2) If the analysis of a system results in 3 or more equations in 3 or more unknowns:

d: the analysis can typically be handled by progressing through the equations, eliminating the number of equations and unknowns one step at a time