Chapter 6, Problem 2SGR

To determine

To find: The given statement is true or false. If false, replace underlined term to make a true sentence.

Answer to Problem 2SGR

The given statement is true.

Explanation of Solution

Given information:

The given statement: If a consistent system has exactly two solution(s), it is said to be independent.

Concept used:

If a system has at least one solution, then it is said to be consistent. If a consistent system of equations has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent, when graphed such equations, represent the same line. If a system has no solution, it is said to be inconsistent .The graphs of such equations do not intersect, i.e., graphs are parallel.

Let we consider a system of equations is $x^2+y=3$ and $-x+y=1$ , the there are two solutions of this system so system is consistent. Since, one equation is quadratic so the system can have at most two solution as shown in Figure-1) and so the solutions are independent.

If a system of equations consists of linear equations there can be only one solution, if there exists two solutions then they are dependent solutions.

Thus, the given statement is true.

Conclusion:

The given statement is true.