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.