The position equation is v and the values are

.

By substituting the above three values of t and s into the position of equation, you can obtain three linear equations in .

When t = 1:

When t = 2:

When t = 3: .

The system of linear equations are

                                               (Equation 1)

                                               (Equation 2)

                                               (Equation 3)

The leading of coefficient of the first equation is one, you can begin by saving the a at the upper left and eliminating the other a - terms from the first column.So, adding negative two times the first equation to the second equation produces a new second equation.

So, the new system of equations are

                                               (Equation 1)

                                               (Equation 2)

                                               (Equation 3)

Adding negative nine times the first equation to the third equation produces a new third equation.

So, the new system of equations are

                                               (Equation 1)

                                               (Equation 2)

                                        (Equation 3)

Adding 6 times the second equation to the third equation produces a new third equation.

So, the new system of equations are

                                               (Equation 1)

                                               (Equation 2)

                                                                 (Equation 3)

Multiplying the second equation by produces a new second equation and multiplying the third equation by produces a new third equation.

So, the new system of equations are

                                               (Equation 1)

                                                     (Equation 2)

                                                                   (Equation 3)

By back - substituting into equation 2, you can solve for , as follows:

                                                     (Write equation 2)

                                                   (Substitute )

                                                                 (Simplify)

By back - substituting into equation 1, you can solve for a, as follows:

                                               (Write equation 1)

                                        (Substitute )

                                                          (Simplify)

                                                               (Subtract 96 from each side)

The solution in ordered triple form is .

The above solution substitute in a position equation of

.

The position equation is .