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 = 6t − 7, where t is any real number. (Enter your answer as a comma-separated list of equations.)

Answer 1

part 1

6x1 - x2 =7, 6x2 - x2 -7 =0

Part 2

x1 = (t + 7)/6

Explanation:

The parametric representation defines a single equation in two variables

x1=t

6x1 = 6t

6x1 - 7 = 6 t- 7 = x2

So the equation is

6x1 - x2 - 7 = 0

or

6x1 - x2 = 7

or

x2 = 6x1 - 7

or

x2 = 6t - 7 = 6x1 - 7

Part 2

if x2 = t

then,

t = 6x1 - 7

t + 7 = 6x1

x1 = (t + 7)/6