Which of the following is a characteristic of a system of linear equations that
Practice Questions
Q1
Which of the following is a characteristic of a system of linear equations that has a unique solution?
The equations are dependent.
The equations are inconsistent.
The equations intersect at one point.
The equations are parallel.
Questions & Step-by-Step Solutions
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.
