Question

how many solutions does the system of equations below have?
y = -8x - 9
y = -8x + \frac{5}{4}
no solution
one solution
infinitely many solutions
submit

Explanation:

Step1: Analyze the equations' slopes and y-intercepts

The two equations are in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the first equation \(y=-8x - 9\), the slope \(m_1=-8\) and the y - intercept \(b_1=-9\). For the second equation \(y=-8x+\frac{5}{4}\), the slope \(m_2 = - 8\) and the y - intercept \(b_2=\frac{5}{4}\).

Step2: Determine the relationship between the lines

Since the slopes of the two lines (\(m_1=-8\) and \(m_2 = - 8\)) are equal, but the y - intercepts (\(b_1=-9\) and \(b_2=\frac{5}{4}\)) are different, the two lines are parallel and do not intersect.

Answer:

no solution