Question

y = -x\
y = 4\
which describes the system of equations above?\
consistent and dependent\
consistent and independent\
inconsistent

Explanation:

Step1: Analyze the equations

The system of equations is \( y = -x \) (a linear equation with slope -1, y-intercept 0) and \( y = 4 \) (a horizontal line, slope 0, y-intercept 4).

Step2: Determine the nature of the system

To find if they intersect, we can solve the system. Substitute \( y = 4 \) into \( y = -x \), we get \( 4 = -x \), so \( x = -4 \). So there is one unique solution \((-4, 4)\).

A consistent system has at least one solution. An independent system has exactly one solution (the lines intersect at one point, not coinciding or parallel). Since these two lines (one with slope -1, one with slope 0) are not parallel (different slopes) and not coinciding, they intersect at one point, so the system is consistent and independent.

Answer:

consistent and independent