To determine whether the given system of linear equations has infinitely many solutions, let's analyze what this implies mathematically.
A system of linear equations has infinitely many solutions if the equations in the system are dependent. This means that one equation can be expressed as a scalar multiple of another. When this happens, the equations are essentially the same line in the coordinate plane, and every point on this line is a solution to the system.
Here are the possible types of solutions for a system of linear equations:
1. Unique solution: The lines intersect at exactly one point.
2. No solution: The lines are parallel and do not intersect.
3. Infinitely many solutions: The lines are the same line, implying they coincide exactly.
In the context of the system given in the question, it is stated that there are infinitely many solutions. This occurs when:
- The equations are proportional.
- After reduction, one equation can be transformed into another, resulting in an identity such as [tex]\(0 = 0\)[/tex] or a statement that holds true for all values of the variables involved.
Thus, the statement claiming that the system of linear equations has infinitely many solutions is:
True.
