Question

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

Answer 1

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.

Answer 2

Answer:

Answer Expert Verified

0

scme1702

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.

Step-by-step explanation: