Chapter 6.1, Problem 49HP

To determine

Explain whether a system of two linear equations with $(0,0)$ and $(2,2)$ as solutions sometimes, always, or never has other solutions.

Answer to Problem 49HP

The system of two linear equations with $(0,0)$ and $(2,2)$ are always other solutions.

Explanation of Solution

Given:

It is given in the question that a system of two linear equations with $(0,0)$ and $(2,2)$ as solutions sometimes, always, or never has other solutions.

From the statement, if two different points are in the solution set for a system of two linear equations, then both lines must pass through both points. For that to be true, they must be the same line .If they are the same line, there are an infinite number of solutions (all other points on the lines).There are always other solutions.