Question

He coordinates below represent two linear equations.

How many solutions does this system of equations have?

Line 1
x y
–3 5
0 4
Line 2
x y
0 4
6 2
A.
0

B.
exactly 1

C.
exactly 2

D.
infinitely many

Answer 1

`\hbox{Line 1:}\\ m=(5-4)/(-3-0)\\ m=(1)/(-3)\\ m=-(1)/(3)\\\\ \hbox{Line 2:}\\ m=(4-2)/(0-6)\\ m=(2)/(-6)\\ m=-(1)/(3)`

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