Question

how many solutions does the system of equations below have?
$y = 2x - 8$
$y = \frac{3}{8}x - \frac{9}{10}$
no solution
one solution
infinitely many solutions
submit

Explanation:

Step1: Analyze the slopes of the 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 \(y = 2x-8\), the slope \(m_1=2\). For the second equation \(y=\frac{3}{8}x - \frac{9}{10}\), the slope \(m_2=\frac{3}{8}\).

Step2: Compare the slopes

Since \(m_1 = 2\) and \(m_2=\frac{3}{8}\), and \(2
eq\frac{3}{8}\). When two lines have different slopes, they are not parallel and will intersect at exactly one point. So the system of equations has one solution.

Answer:

one solution