Which answer best describes the system of equations shown in the graph?

Question

Responses

Consistent and dependent
Consistent and dependent

Consistent and independent
Consistent and independent

Inconsistent
Inconsistent

Not enough information
Not enough information
Number graph ranging from negative seven to eight on the x and y axes. A line is drawn on the graph that crosses the x axis at begin ordered pair negative three comma zero end ordered pair and crosses the y axis at begin ordered pair zero comma five end ordered pair. A second line is drawn on the graph, which crosses the y axis at begin ordered pair zero comma three end ordered pair and crosses the x axis at begin ordered pair four comma zero end ordered pair.

Answer 1

To determine the relationship between the two lines represented in the system of equations from the graph you described, we need to analyze their characteristics:

1. Identifying the Lines:

   • The first line crosses the x-axis at (-3, 0) and the y-axis at (0, 5).
   • The second line crosses the y-axis at (0, 3) and the x-axis at (4, 0).

2. Characteristics of the Lines:

   • Since both lines have different intercepts and slopes (the first line has a slope different from the second line), they will intersect at a single point.

3. Classification of the System:

   • A system of equations can be classified as:
     • Consistent and Independent: If the lines intersect at a single point (one unique solution).
     • Consistent and Dependent: If the lines are the same line (infinitely many solutions).
     • Inconsistent: If the lines are parallel and do not intersect (no solutions).

Given that the two lines intersect at one point, the best description for the system of equations represented by these lines is:

Consistent and independent.