Q:

The graph plots four equations, A, B, C, and D: Line A joins ordered pair negative 6, 16 and 9, negative 4. Line B joins ordered pair negative 2, 20 and 8, 0. Line C joins ordered pair negative 7, negative 6 and 6, 20. Line D joins ordered pair 7, 20 and 0, negative 7. Which pair of equations has (4, 8) as its solution? Equation A and Equation C Equation B and Equation C Equation C and Equation D Equation B and Equation D'

Accepted Solution

A:
Answer:The pair of equations which has (2,12) as its solution is,equation B and equation C.                             Step-by-step explanation:According to the question,equation of line A is $$\frac {y - 16}{x + 6} = \frac {16 + 4}{-6 - 9}$$                             or, $$\frac {y - 16}{x + 6} = \frac {-4}{3}$$                             or, $$3y - 48 = -4x - 24$$                             or, 3y + 4x = 24 ------------------(1)Now, the point (2, 12) doesn't satisfy (1). Hence, (2,12) is not a solution for the line A.Equation of line B is, $$\frac {y - 20}{x + 2} = \frac {20 - 0}{-2 - 8}$$                               or, $$\frac {y - 20}{x + 2} = -2$$                               or, $$y - 20 = -2x - 4$$                               or, y + 2x = 16  -----------------------------(2)The point (2,12) is satisfied by (2). Hence, (2, 12) is a solution for line B.Equation of line C is, $$\frac {y + 6}{x + 7} = \frac {20 + 6}{6 + 7}$$                               or, $$\frac {y + 6}{x + 7} = 2$$                               or, y + 6 = 2x + 14                               or. y - 2x = 8 -----------------------------------(3)The point (2, 12) is satisfied by (3). Hence, (2 , 12) is a solution for the line C.Equation of line D is, $$\frac {y - 20}{x - 7} =\frac {20 + 7}{7 - 0}$$                                or, $$\frac {y - 20}{x - 7} = \frac {27}{7}$$                                or, 7y - 140 = 27x - 189                                or, 7y  - 27x = -49----------------------------------------(4)The point (2, 12) is not satisfied by (4). hence, (2, 12) is not a solution of the line DHence, the pair of equations which has (2,12) as its solution is,equation B and equation C.