Question

y = x + 2\
y = x + 1\
which describes the system of equations above?\
consistent and dependent\
consistent and independent\
inconsistent

Explanation:

Step1: Analyze the slopes

The two equations are \( y = x + 2 \) and \( y = x + 1 \). The slope-intercept form is \( y = mx + b \), where \( m \) is the slope. For both equations, the slope \( m = 1 \).

Step2: Analyze the y-intercepts

The y-intercept \( b \) for \( y = x + 2 \) is \( 2 \), and for \( y = x + 1 \) is \( 1 \). Since the slopes are equal (parallel lines) and y-intercepts are different, the lines never intersect.

Step3: Determine the system type

A system of linear equations is inconsistent if there are no solutions (parallel lines with different y-intercepts), consistent and independent if there is one solution (intersecting lines), and consistent and dependent if there are infinitely many solutions (same line). Since these lines are parallel and distinct, there are no solutions, so the system is inconsistent.

Answer:

inconsistent