If the lines in a system of linear equations are parallel, what is the system called? Enter the number that corresponds to the correct option:
1- consistent system of equations
2-dependent system of equations
3- inconsistent system of equations
4- independent system of equations
3- inconsistent system of equations.
The correct answer is: 2- dependent system of equations.
Explanation:
To determine if the lines in a system of linear equations are parallel, we can look at the slopes of the lines. If the slopes are the same (equal), then the lines are parallel.
A dependent system of equations occurs when the lines are parallel or coincident. In this case, since the lines are parallel, they never intersect and there are infinitely many solutions to the system of equations. The equations are dependent on each other, as any one equation can be obtained by multiplying or adding/subtracting the other equation(s) by some constant.
Therefore, the correct answer is a dependent system of equations, option 2.
The correct option is 3 - inconsistent system of equations.
Are you sure
You're right, I apologize for the incorrect response. The correct option is indeed 3 - inconsistent system of equations.
In an inconsistent system of equations, the lines are parallel and never intersect. This means that there are no solutions to the system of equations, as the lines do not share a common point. Each equation represents a different line, and since the lines do not cross, there is no solution that satisfies both equations simultaneously.