Question

1. if the system of equations $y = 3x + 5$ and $y = 3x + 5$ is solved, what type of solution do we expect?

a. one solution
b. infinitely many solutions
c. no solution
d. undefined solution

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

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

Explanation:

Step1: Analyze first system

The two equations are identical: $y=3x+5$ and $y=3x+5$. Every point on the line satisfies both equations, so there are infinitely many solutions.

Step2: Define independent system

An independent system of linear equations has exactly one unique solution, which occurs when the lines intersect at a single point.

Answer:

1. b. Infinitely many solutions
2. a. There is one solution