(1) results in the system simultaneous equations with \(3\) unknowns and \(3\) equations. Sufficient.

(2) the same is true: \(3\) unknowns and \(3\) equations. Sufficient.

Answer: D
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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
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There are 3 equation and 4 variable(x,y,m,b). Knowing values of any one variable will help us solve this question.

NOTE - We need not solve the equation to find the values. We just need to determine if it is possible to find the value of m + b.

Statement 1 :- The x−coordinate at the point where all three lines meet is 8.

This gives the value of x =8. Hence we can solve the equation to find unique value of m +b. Sufficient.

Statement 2 :- The y−coordinate at the point where all three lines meet is 9.

This gives the value of y =9. Hence we can solve the equation to find unique value of m +b. Sufficient.

Hence Ans -D