1. The coordinates below represent two linear equations.

How many solutions does this system of equations have?

Line 1

x y

-2 7

0 6

Line 2

x y

3 0

0 - 3

A. 0

B. exactly 1

C. exactly 2

D. infinitely many

2. 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

In both questions, we form the equations of both lines.

1)

Line 1:

slope = (6-7) / (0+2) = - 1/2

y-int = 6

y = (-1/2) x + 6

Line 2:

slope = (-3-0) / (0-3) = 1

y-int = - 3

y = x - 3

The equations are not dependent because one cannot be formed from the other by multiplying by a constant; neither are they parallel. Therefore, the answer is B, exactly one.

2)

Line 1:

slope = (4-3) / (-2+4) = 1/2

4 = (1/2) (-2) + c

y-int = 5

y = (1/2) x + 5

Line 2:

Slope = (6-8) / (2-0) = - 1

y-int = 8

y = - x + 8

The equations are independent and not parllel so the answer is B, exactly 1 solution.