Solution
Given:• The equations of three lines are:
o y = mx – 7… equation 1
o y = 12x + b … equation 2
o y = x + 1 … equation 3
• The three lines intersect at exactly one point
To find:• The value of (m + b)
Analysing Statement 1• As per the information provided in statement 1, the x−coordinate at the point where all three lines meet is 8
o If we put x = 8 at equation 3, we will get y
o Putting the values of both x and y in equations 1 and 2, we will get the values of m and b respectively
o Therefore, we can find out the value of m + b
Hence, statement 1 is sufficient to answer
Analysing Statement 2• As per the information provided in statement 2, the y−coordinate at the point where all three lines meet is 9
o If we put y = 9 at equation 3, we will get x
o Putting the values of both x and y in equations 1 and 2, we will get the values of m and b respectively
o Therefore, we can find out the value of m + b
Hence, statement 2 is sufficient to answer
Hence, the correct answer is option D.
Answer: D