Question

how many solutions does the system of equations below have?
y = -5x - 6
y = -5x + \frac{6}{7}
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 \(y=-5x - 6\), the slope \(m_1=-5\) and the y - intercept \(b_1=-6\). For the second equation \(y=-5x+\frac{6}{7}\), the slope \(m_2 = - 5\) and the y - intercept \(b_2=\frac{6}{7}\).

Step2: Determine the relationship between the lines

Since the slopes of the two lines (\(m_1=m_2=-5\)) are equal and the y - intercepts (\(b_1
eq b_2\)) are different, the two lines are parallel. Parallel lines do not intersect.

Answer:

no solution