Question

Three systems of linear equations are shown.For each system, choose the best description of its solution.If the system has exactly one solution, give its solution.

Answer 1

• A: The system has exactly one solution, the solution is (-3, 0).

,

• B: The system has no solutions.

,

• C: The system has infinitely many solutions.

Explanation:

System A

A system of equations is said to be consistent if it has solutions. When a consistent system has exactly one solution, it is independent. These systems form an X-shape when graphed.

Since the graph of system A forms an X-shape, the system has exactly one solution.

The solution is (-3, 0).

System B

An inconsistent system has no solutions. They form parallel lines.

The system of equations in B has no solution.

System C

Both equations form the same line, therefore, the system of equations in C has infinitely many solutions.