Question

Suppose that when a system of linear equations is graphed, one line completely overlaps the other line. Which statement is correct?
1. The system of equations has one solution because the lines intersect at one point.
2. The system of equations has one solution because the lines do not intersect at only one point.
3. The system of equations does not have only one solution because the lines intersect at one point.
4. The system of equations does not have only one solution because the lines do not intersect at only one point.

Answer 1

I believe the answer is 4. The system of equations does not have only one solution because the lines do not intersect at only one point. I just took the quiz.

Answer 2

The true statement is (4) the system of equations does not have only one solution because the lines do not intersect at only one point.

From the question, we understand that the linear equations overlap.

This means that, the linear equations in the system are equivalent

Take for instance, the following systems of linear equations

• $\mathbf{2x + y = 1}$ and $\mathbf{y = 1 - 2x}$.
• $\mathbf{x + y = 2}$ and $\mathbf{2x + 2y =2}$.
• $\mathbf{y - 7 = x}$ and $\mathbf{y = x + 7}$.

The graphs of the above systems of equations would overlap, because they are equivalent equations.

This also means that, the graph would have multiple points of intersection

Hence, the true statement is (4)

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