Questions: Select the correct choice that completes the sentence below. If a system of linear equations in two variables has two graphs that coincide, there is/are □ solution(s) to the system.

Select the correct choice that completes the sentence below. If a system of linear equations in two variables has two graphs that coincide, there is/are □ solution(s) to the system.

Transcript text: Select the correct choice that completes the sentence below. If a system of linear equations in two variables has two graphs that coincide, there is/are $\square$ solution(s) to the system.

Solution

Solution Steps

Step 1: Understanding Coinciding Lines

When two linear equations in two variables are represented graphically, if their graphs coincide, it means they are the same line. This implies that every point on this line satisfies both equations.

Step 2: Analyzing Solutions

For a system of linear equations represented by coinciding lines, there are not just a finite number of solutions, but rather an infinite number of solutions. This is because any point $(x, y)$ on the line is a solution to the system.

Step 3: Conclusion

Thus, the conclusion is that the system has infinitely many solutions.