SOLUTION: Determine the solution set for the following system. If infinitely many solutions, express answer in terms of t and s. 2x1-3x2+x3-7x4=23 (These are sub numbers)

Question 1122637: Determine the solution set for the following system. If infinitely many solutions, express answer in terms of t and s.
2x1-3x2+x3-7x4=23 (These are sub numbers)
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

One equation with four unknowns -- of course there are infinitely many solutions.

Presumably your "t and s" are parameters which we are to use to write the solution set. But two parameters is not enough.

With one equation and two unknowns, we can write a solution set using one parameter. For example:

3x+5y = 30

let x = t; then
5y = 30-3t
y = (30-3t)/5
y = (30-3t)/5

The solution set is
x = t; y = (30-3t)/5

Similarly with one equation and three unknowns we can define the solution set using two parameters; for example

a+b-c = 10
c = 10-a-b

The solution set is
a = s; b = t; c = 10-s-t

For one equation and four unknowns, we would need three parameters....

I am not familiar with any uses of parametric equations using even two parameters, much less three.

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"....
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