Verified answer

the idea is to solve the given set of equations, however there are only 2 sets of equations for 3 variables, means there is one degree of freedom for the entire set.

The technique is to solve the equation in termsof x

5x-y+2z=5

-x+2y-3z=8

rewrite as

-y+2z=5-5x

2y-3z=8+x

treat x as a constant, you will get the solution in the form

y=a+bx, z=c+dx

solving for y and z in terms of x

z=18-9x

y=31-13x

let x=t

the parametric equation is

x=t

y=31-13t

z=18-9t

x^2 + y^2 = a million has parametric equation: x = cos(t) y = sin(t) Intersection of x^2 + y^2 = a million and x + y + z = a million (z = a million - x - y) : x = cos(t) y = sin(t) z = a million - cos(t) - sin(t) ????m?m