Question

The coordinates below represents two linear equations
how many solutions does this system have

Line 1. Line 2
X y X. Y
-3 5 0. 4
0 4. 6. 2
I now it is not a
A 0
B exactly 1
C exactly 2
D infinatly

Answer 1

$\hbox{Line 1:}\\ m=\frac{5-4}{-3-0}\\ m=\frac{1}{-3}\\ m=-\frac{1}{3}\\\\ \hbox{Line 2:}\\ m=\frac{4-2}{0-6}\\ m=\frac{2}{-6}\\ m=-\frac{1}{3}$

Both lines have the same slope so they're parallel. They also pass through the same point $(0,4)$. That means they're overlapping, so there is infinitely many solutions.