Question

Find a system of two equations in three variables x1, x2, and x3, that has the solution set given by the parametric representation x1=t, x2=s and x3=3+s-t, where s and t are any real numbers. Then show that the solutions to your system can also be written as x1=3+s-t, x2=s and x3=t

Answer 1

If we add the three variables
x1 + x2 + x3
and substitute the solutions
x1 + x2 + x3 = t + s + 3 + s - t
We can rearrange the right side to show that the solutions can also be written as x1=3+s-t, x2=s and x3=t

x1 + x2 + x3 = (3 + s - t) + (s) + (t)
Which will give us
x1=3+s-t
x2=s
x3=t