Question

The coordinates below represent two linear equations.



How many solutions does this system of equations have?




Line 1
x y
–1 6
0 4

Line 2
x y
0 7
1 5












A. 0








B. exactly 1








C. exactly 2








D. infinitely many

Answer 1

Use point-slope form to write an equation for each line.

line 1
m = (4-6)/(0--1) = -2
y - (4) = -2 (x - (0))
y - 4 = -2x
y = -2x + 4


line 2
m = (5-7)/(1-0) = -2
y - (7) = -2(x - (0))
y - 7 = -2x
y = -2x + 7

Since both lines have the same slope (-2) they are parallel and thus do not intersect. So, there are no solutions.