Answer
Yes
Work Step by Step
Consider the first equation $t^2-4t+3=0...(1)$
This gives : $t^2--3t-t+3=0 \implies t= 3$
Consider the second equation $t^2-7t+12=0 ....(2)$
This gives: $t^2-6t-t+12=0 \implies t= 3$
Need to set the $z$ component of the two equations equal to each other first.
By doing so, we have $t^2=5t-6$ ...(3)
This gives: $t^2-5t+6=0 $
and $t^2-6t+t+6=0$
Then, we have $t=3$
Yes, all the three equations gives three equations.
