Question

determine if the system of equations is consistent or inconsistent. if it is consistent, is it dependent or independent and name the solutions. 1. graph 1 2. graph 2 4. graph 3 graph 4

Explanation:

Step1: Analyze Graph 1

Two lines intersect at $(-2, -1)$. A consistent system has at least one solution; independent systems have exactly one unique solution.

Step2: Analyze Graph 2

Two lines intersect at $(2, 3)$. This system has one unique solution, so it is consistent and independent.

Step3: Analyze Graph 3

Two lines are parallel (no intersection). Inconsistent systems have no solutions.

Step4: Analyze Graph 4

Two lines are parallel (no intersection). This system has no solutions, so it is inconsistent.

Answer:

1. Consistent and Independent; Solution: $(-2, -1)$
2. Consistent and Independent; Solution: $(2, 3)$
3. Inconsistent; No solutions
4. Inconsistent; No solutions