Question

y = -2 y = 5 which describes the system of equations above? consistent and dependent consistent and independent inconsistent

Explanation:

Step1: Recall system of equations types

A system of linear equations can be:

• Consistent and dependent: If the lines are coincident (same line), infinite solutions.
• Consistent and independent: If the lines intersect at one point, one solution.
• Inconsistent: If the lines are parallel (no intersection), no solution.

Step2: Analyze the given lines

The equations are \( y = -2 \) and \( y = 5 \). These are horizontal lines (since they have the form \( y = k \), where \( k \) is a constant). Horizontal lines have a slope of \( 0 \). Since both lines have the same slope (\( 0 \)) and different \( y \)-intercepts (\( -2 \) and \( 5 \)), they are parallel.

Step3: Determine the type of system

Parallel lines never intersect, so there is no solution to the system. A system with no solution is called inconsistent.

Answer:

inconsistent