Question

Find a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1 = t and x2 = 5t − 6, where t is any real number. (Enter your answer as a comma-separated list of equations.)

Answer 1

The required system of equations to the given parametric equations are:

5x1 - x2 = 6

x1 + x2 = -6

Explanation:

Given the parametric equations:

x1 = t

x2 = -6 + 5t

Eliminating the parameter t, we obtain one of the equations of a system in two variables, x1 and x2 that has the solution set given by the parametric equations.

Doing that, we have:

5x1 - x2 = 6

Again a second equation can be a linear combination of x1 and x2

x1 + x2 = -6 + 6t

x1 + x2 = -6 (putting t=0)

And they are the required equations.