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.
