Question

how many solutions does the system of equations below have?
y = -3x + \frac{5}{8}
y = -3x - \frac{7}{8}
no solution
one solution
infinitely many solutions

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 \(y=-3x+\frac{5}{8}\), the slope \(m_1=-3\). For the second equation \(y = - 3x-\frac{7}{8}\), the slope \(m_2=-3\). Since \(m_1 = m_2\), the two lines are parallel.

Step2: Analyze the y - intercepts of the two lines

The y - intercept of the first line \(b_1=\frac{5}{8}\) and the y - intercept of the second line \(b_2 =-\frac{7}{8}\). Since \(b_1
eq b_2\), the two parallel lines are distinct and will never intersect.

Answer:

no solution