Respuesta :
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 [tex]\frac {y - 16}{x + 6} = \frac {16 + 4}{-6 - 9}[/tex]
or, [tex]\frac {y - 16}{x + 6} = \frac {-4}{3}[/tex]
or, [tex] 3y - 48 = -4x - 24[/tex]
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, [tex]\frac {y - 20}{x + 2} = \frac {20 - 0}{-2 - 8}[/tex]
or, [tex]\frac {y - 20}{x + 2} = -2[/tex]
or, [tex] y - 20 = -2x - 4[/tex]
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, [tex]\frac {y + 6}{x + 7} = \frac {20 + 6}{6 + 7}[/tex]
or, [tex]\frac {y + 6}{x + 7} = 2[/tex]
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, [tex]\frac {y - 20}{x - 7} =\frac {20 + 7}{7 - 0}[/tex]
or, [tex]\frac {y - 20}{x - 7} = \frac {27}{7}[/tex]
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 D
Hence, the pair of equations which has (2,12) as its solution is,
equation B and equation C.
