Question

how many solutions does the system of equations below have?
$y = \frac{-3}{10}x - 2$
$y = \frac{-3}{10}x - \frac{5}{8}$
no solution
one solution
infinitely many solutions

Explanation:

Step1: Analyze the slopes of the lines

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 \(y=\frac{-3}{10}x - 2\), the slope \(m_1=-\frac{3}{10}\) and the y - intercept \(b_1=-2\). For the second equation \(y = \frac{-3}{10}x-\frac{5}{8}\), the slope \(m_2=-\frac{3}{10}\) and the y - intercept \(b_2 =-\frac{5}{8}\). Since \(m_1=m_2\) (the lines are parallel) and \(b_1
eq b_2\) (the lines are not coincident), the two lines do not intersect.

Step2: Determine the number of solutions

A system of linear equations represents the intersection of two lines. If two lines are parallel and not coincident, they never intersect, so the system of equations has no solution.

Answer:

no solution