Question

how many solutions does the system of equations below have?
$y = -4x - 4$
$y = -4x - \frac{4}{9}$
no solution
one solution
infinitely many solutions
submit

Explanation:

Step1: Analyze the slopes of the two lines

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

Step2: Determine the relationship between the lines

Since the slopes of the two lines are equal (\(m_1=m_2=-4\)) and the y - intercepts are different (\(b_1=-4
eq b_2 =-\frac{4}{9}\)), the two lines are parallel. Parallel lines do not intersect, so the system of equations has no solution.

Answer:

no solution