Question

how many solutions does the system of equations below have?
$y = \frac{5}{8}x + \frac{4}{3}$
$y = \frac{5}{8}x + \frac{4}{3}$
no solution
one solution
infinitely many solutions

Explanation:

Step1: Identify slope and intercepts

The two equations are $y = \frac{5}{8}x + \frac{4}{3}$ and $y = \frac{5}{8}x + \frac{4}{3}$. They share identical slopes $\frac{5}{8}$ and identical y-intercepts $\frac{4}{3}$.

Step2: Classify system consistency

Systems with matching slopes and intercepts are coinciding lines, meaning every point on the line is a solution.

Answer:

infinitely many solutions