Question 1122637
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One equation with four unknowns -- of course there are infinitely many solutions.<br>
Presumably your "t and s" are parameters which we are to use to write the solution set.  But two parameters is not enough.<br>
With one equation and two unknowns, we can write a solution set using one parameter.  For example:<br>
3x+5y = 30<br>
let x = t; then
5y = 30-3t
y = (30-3t)/5
y = (30-3t)/5<br>
The solution set is
x = t; y = (30-3t)/5<br>
Similarly with one equation and three unknowns we can define the solution set using two parameters; for example<br>
a+b-c = 10
c = 10-a-b<br>
The solution set is
a = s; b = t; c = 10-s-t<br>
For one equation and four unknowns, we would need three parameters.... <br>
I am not familiar with any uses of parametric equations using even two parameters, much less three.<br>
It seems rather pointless.  You are saying "choose any 3 values for 3 of the variables and use them to determine the value of the fourth"....