Question

The coordinates below represent two linear equations.

How many solutions does this system of equations have?


Line 1
x y
–4 3
–2 4

Line 2
x y
0 8
2 6





A.


0


B.


exactly 1


C.


exactly 2


D.


infinitely many

Answer 1

B

Explanation:

The lines intersect at exact one point. This is true because the lines do not have the same slope. This means the lines are not parallel and must cross at one point.

Calculate slope for Line 1 by
`(y_2-y_1)/(x_2-x_1)` where
`x_2=-4\\ y_2=3` and
`x_1=-2\\y_1=4`.

`(y_2-y_1)/(x_2-x_1)=(3-4)/(-4--2)=(-1)/(-4+2)=(-1)/(-2)=(1)/(2)`

Calculate slope for Line 2 by
`(y_2-y_1)/(x_2-x_1)` where
`x_2=2\\ y_2=6` and
`x_1=0\\y_1=8`.

`(y_2-y_1)/(x_2-x_1)=(6-8)/(2-0)=(-2)/(2)=-1`