Question

how many solutions does the system of equations below have?
$y = -3x + 5$
$y = \frac{5}{7}x + \frac{7}{2}$
no solution
one solution
infinitely many solutions

Explanation:

Step1: Compare slopes

The first equation has slope $m_1=-3$, the second has $m_2=\frac{3}{7}$. $-3
eq \frac{3}{7}$.

Step2: Classify system

Two linear equations with different slopes intersect once.

Answer:

one solution