Question

y = 4x - 1\
y = 4x - 9\
which describes the system of equations above?\
consistent and dependent\
consistent and independent\
inconsistent

Explanation:

Step1: Analyze the slopes and y - intercepts

The two equations are in the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y = 4x-1\), the slope \(m_1 = 4\) and the y - intercept \(b_1=- 1\). For the equation \(y = 4x - 9\), the slope \(m_2=4\) and the y - intercept \(b_2=-9\).

Step2: Determine the type of system

Since the slopes of the two lines are equal (\(m_1 = m_2=4\)) and the y - intercepts are different (\(b_1
eq b_2\)), the two lines are parallel. A system of linear equations with parallel lines has no solution. A system of equations with no solution is called an inconsistent system. But wait, let's re - check. Wait, the two lines \(y = 4x-1\) and \(y = 4x - 9\) are parallel (same slope, different y - intercepts). So they never intersect, which means there is no solution. So the system is inconsistent.

Answer:

inconsistent