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Solution


Q.

For the equations 2x + y = 8 and 4x + 2y = 10, select the correct statements:

(i) The lines are identical.
(ii) The lines are parallel.
(iii) The second equation can be reduced to 2x + y = 5.
(iv) There is no solution to this system.
1 (i), (iii) and (iv)  
2 (i), (ii), (iii) and (iv)  
3 (ii), (iii) and (iv)  
4 (i) and (iv)  

Ans.

(3)

We have, 2x + y = 8 …(i)
And, 4x + 2y = 10 ⇒ 2(x + y) = 2×5 ⇒ 2x + y = 5.
Here, a?/a? = 2/2 = 1, b?/b? = 1/1 = 1, c?/c? = 8/5.
Since a?/a? = b?/b? ≠ c?/c?, the lines are parallel. So, there is no point of intersection.
Hence, no solution.