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12 April, 03:26

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

+2
Answers (1)
  1. 12 April, 05:51
    0
    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.
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