Question

if the slopes of two linear equations are the same, the lines will be ______, unless they have the same y-intercept.
when a system of linear equations can be satisfied by any number of ordered pairs, it is considered to have ______ solutions.
in a scenario where no set of values satisfies both equations of a system, the system is labeled as ______.

Explanation:

1. For linear equations, same slopes mean lines are parallel; if they share the same y-intercept, they are coincident (the same line) instead.
2. A system of linear equations with infinitely many solutions is dependent, meaning all ordered pairs on one line satisfy both equations.
3. An inconsistent linear system has no overlapping solutions, as the lines are parallel and distinct with no intersection.

Answer:

1. parallel
2. infinitely many
3. inconsistent