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

Question

Xander Vance

Mathematics

18 October, 10:28

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

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Answers (1)

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Kallie Mcbride · 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