Question

1. how many solutions does the system of equations below have?

y = \frac{-3}{5}x + \frac{6}{9}
y = \frac{-4}{9}x + \frac{8}{9}
no solution
one solution
infinitely many solutions

Explanation:

Step1: Compare slopes of the lines

The first line has slope $m_1 = \frac{4}{5}$, the second has slope $m_2 = \frac{4}{9}$. Since $\frac{4}{5}
eq \frac{4}{9}$, the lines are not parallel.

Step2: Determine solution count

Non-parallel linear lines in a plane intersect at exactly one point, so the system has one solution.

Answer:

one solution