Task is: Examine the system of linear equations for solvability. If it has infinitely many solutions

[slow sleet]

The last sentence was supposed to be: If it has infinitely many solutions, determine the solution vector.

[lyric garden]

Well first one is unsolvable because we lack one more equation

4 unknowns :(x1, x2, x3, t) against 3 equations

b) can’t be solved either. Why? Look at the number of unknowns and number of equations.

c) on the other hand can be solved !

We have an info on z.( z=4)

Let me know if you understand why a) and b) are not solvable @slow sleet

[slow sleet]

but what can t be so it can be solvable or infinitely solvable

[lyric garden]

Ohhh t is a parameter then

Not an unknown

Okay so what i propose is doing some checks for each equation within a system.

Lets hop on a)
Lets start with the equation:

tx_3=-3