Question

Which of the following is always true of a dependent system of two equations?


The lines are perpendicular.


One of the lines has a positive slope and the other has a negative slope.


The lines intersect at exactly one point.


There are infinitely many solutions.

Answer 1

The only solution that is true about the dependent system of equations is "There are infinitely many solutions".

What is a System of equations?

Inconsistent System

For a  system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of equations to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

As discussed above the Dependent consistent system has infinitely many solutions as their line are coinciding, therefore, the only solution that is true about the dependent system of equations is "There are infinitely many solutions".

Learn more about the System of equations:

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