Question

What is the solution of the following system -2x-y=1 -4x-2y=-1

Answer 1

-2x - y = 1 (1st)

-4x - 2y  = -1 (2nd)

Multiply 1st equation by 2

-4x - 2y = 2

Now you have 2 new equations

-4x - 2y = 2

-4x - 2y = -1

----------------------Subtract

 0 ≠ 3

Answer: No solutions

Answer 2

Answer:  The correct option is

(B) no solution.

Step-by-step explanation:  We are given to find the solution to the following system of equations :

$-2x-y=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-4x-2y=-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

From equation (i), we have

$-2x-y=1\\\\\Rightarrow y=-2x-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of y from equation (iii) in equation (ii), we get

$-4x-2(-2x-1)=-1\\\\\Rightarrow -4x+4x+2=-1\\\\\Rightarrow 2=-1,$

which can never be possible.

Therefore, the given system of equations has no solution.

Option (B) is CORRECT.