Question

1. what does it mean if a system of equations is called independent?

a. the system has no solutions
b. the equations are the same
c. the lines intersect at multiple points
d. there is one solution

Explanation:

An independent system of equations has exactly one solution. When two lines (in the case of a system of two linear equations) are not parallel (so they are not the same line - which would be a dependent system) and they are not coincident (same line), they intersect at a single point. This single - point intersection represents the one solution of the system.

• Option a: A system with no solutions is called an inconsistent system (the lines are parallel).
• Option b: If the equations are the same, the system is dependent (infinitely many solutions).
• Option c: Lines in a system of linear equations (in a plane) can't intersect at multiple points (unless they are the same line, but that's a dependent system).

Answer:

d. There is one solution