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 [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 DHence, the pair of equations which has (2,12) as its solution is,equation B and equation C.