Answer format for solve()

I don't like the way MuPad inserts an extra parameter in the solution to a problem I gave it:

solve( { v1 + v2*t + v3*t^2 = 0,
v1*-2 + v2*(-2*t+1) + v3*(-2*t^2 + 2*t) = 0,
v1*4 + v2*(4*t-4) + v3*(4*t^2 - 8*t + 2)=12 } )

Answer: {[t = -z/12, v1 = z^2/24, v2 = z, v3 = 6]}

So I have 2 questions here:

1. How do you stop mupad from using a parameter, or remove z from the equations and have the solution in t only?
2. If you square z in the solution for v1, you lose the negativity, so isn't this answer strictly speaking not correct? (Since v1 = 6*t^2, not -6*t^2 as it should be?)

Answer 1

[Walter Roberson]

1. Specify the variable you want to solve for

solve(...,{z,v1,v2,v3})

2. The solution set I get in terms of t is

z = z, v1 = 6*t^2, v2 = -12*t, v3 = 6

If I back-substitute those in to the original equations, I get 6=6 and 12=12 which are logical truths, so v1 = 6*t^2 is correct.

If I back-substitute using v1 = -6*t^2 and the rest the same, I get

-12*t^2 = 0, 24*t^2 = 0, -48*t^2+12 = 12

which is true if and only if t=0

Answer 2

[Andrew Newell]

1. Just specify the variables:

solve(...,{v1,v2,v3})

2. In your solution, if you substitute for all four variables, the equation is zero.