Question

When considering the system (−1x+2y= -13) and (2x−4y=26) What are the solution to the system? If there are infinitely many solutions let y=t and solve for x in terms of t ?

Answer 1

There are infinitely many solutions of the chosen form `x=2t+13` and `y=t`

Explanation:

If we try to solve

`−1x+2y= -13` and `2x−4y=26`

We get a tautology like `13=13` or `0=0` true for all values of the variables.
This implies that every solution of one equation is a solution of the other.

To writ the solutions using `y=t`, substitute for `y` in either equation and solve for `x`.

You will get `x=2t+13`

One way to write the solution set is:

`{(2t+13,t)| t in RR}`