the coordinates below represent two linear equations. how many solutions does this system of equations have?
line 1
x y
–4 8
4 6
line 2
x y
–1 1
3 5
a.
0
b.
exactly 1
c.
exactly 2
d.
infinitely many

This may be one of those questions that could take
more paper to ask than to answer.

Line-1 goes through  (-4, 8) and  (4,6) .

Its slope is (difference in 'y') / (difference in 'x')

Dif in 'y' = (6 - 8) = 2
Dif in 'x' = (4 - -4) = 8
Slope of Line-1 =  2/8  or  1/4

Line-2 goes through  (-1, 1)  and  (3, 5)

Its slope is (difference in 'y') / (difference in 'x')

Dif in 'y' = (5 - 1) = 4
Dif in 'x' = (3 - -1) = 4
Slope of Line-2 = 4/4 = 1

Slope of Line-1 = 1/4
Slope of Line-2 = 4

The slopes of the lines are different.
They can't be parallel, and they can't be the same line.
They must intersect in one point, and only one point.

That means the pair of equations has exactly one (1) solution.
 

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