Expert: Richard J. Raridon - 8/26/2011

Question
Dear Prof Richard

Referring to Definition of Simultaneous equations

http://en.wikipedia.org/wiki/Simultaneous_equations

For example,

x+y=3
x-y=5

The Above case has two variables x & y -> 2

Answer :

x=4
y=-1

Question 1:

Since Simultaneous  equations involves multiple variables, what are the rules for creating Simultaneous equations ?

i.e Are these valid examples ?

1.

x+y+z=3
x-y-z=4

The above involves 3 variables, since there are three variables do we have to have 3 Simultaneous equations to calculate value of x,y & z.
i.e say one more equation to be added

say 2x+2y-5z=1

2.

a+b+c+d=4
2a-b+c-2d=5

The above involves 4 variables, The above involves 4 variables, since there are four variables do we have to have 4 Simultaneous equations to calculate value of x,y & z.

say  3a+2b+2c-d=1
      5a+3b-3c+3d=3

Question 2 :

Can i have both Upper and Lowe case Letters in Simultaneous  Equations ?

are these valid examples ?

Example 1 :

x + X =4
x - X =6

Example 2 :

x + Y = 1
x - Y = 7

Question 3:

Since there are 26 Upper case characters  A.... Z and 26 Lowe case characters a ... z which gives us a count of Total 52 variables
can we construct Simultaneous equations as a example to compute all values of the 52 variables.

So do we have to write 52 Simultaneous equations in this case ?

Thanks & Regards,
Prashant S Akerkar

Answer
In general, you have to have as many equations as you have unknowns.  You can use upper or lower case, Greek letters, whatever.  It is possible to have indeterminate equations and, for example, solve for three variables with only two equations if you know the answers have to be integers.