Which of the following is a characteristic of a system of linear equations that

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Question: Which of the following is a characteristic of a system of linear equations that has a unique solution?

Options:

Correct Answer: The equations intersect at one point.

Solution:

A unique solution occurs when the equations intersect at exactly one point.

Which of the following is a characteristic of a system of linear equations that has a unique solution?

Which of the following is a characteristic of a system of linear equations that has a unique solution?

Step 1: Understand what a system of linear equations is. It is a set of two or more equations with the same variables.
Step 2: Know that each equation represents a line when graphed on a coordinate plane.
Step 3: A unique solution means that the lines intersect at exactly one point.
Step 4: If the lines intersect at one point, it means there is one set of values for the variables that satisfies all equations.
Step 5: If the lines are parallel, they do not intersect, and if they are the same line, they intersect at infinitely many points. Both of these cases do not have a unique solution.

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