Chapter 6.3, Problem 34HP

To determine

To describe the solution of a system of equations if the result was 0 = 0 after adding the two equations

Explanation of Solution

If the given statement is true:

There would be infinite number of solutions. The system will be consistent and dependent. Both the equations represent the same line.

For example,

Consider $2x+5y=4$ and $-2x-5y=-4.$

When both the equations added, the result is 0 = 0 since the variables are eliminated.

This system would have infinitely many solutions.