Which of the following statements is true?

Option A - (0,0) is a solution to both the equations. is the only true statement.

Step-by-step explanation:

Step 1 :    

Given  2 equations are

n = m

n = 4m

Step 2:

(0,0) is a solution to both the equations.

This statement is true as substituting the point , the equations are true.

Step 3 :

Every solution to n=m is also a solution to n=4 m

Take the point (5,5)

This point lies on the equation n = m, as both the x and y co ordinates are same

n = 4 m = 4 × 5 = 20

So here for n = 5, n = 4 m is not true and hence this point is not a solution for the second equation thought it is a solution for the first equation

Hence this statement is not true

Step 4:

The graph of the solutions is  parallel lines

this statement is not true because the 2 lines intersect at (0,0) as observed from step 2.

Step 5 :

No point on the line n=m is also a point on n=4 m

This statement is not true because (0,0) is a point on both the lines.

Step 6 :

Answer :

Option A - (0,0) is a solution to both the equations. is the only true statement.