Question

Check which of the following are solutions of the equation 2x – y = 6 and which are not :

(1) (3, 0)    (2) (0, 6)    (3) (2, −2)     (4) (√3, 0 )    (5) `(1/2,-5)`

Answer 1

In the equation 2x - y = 6 we get 

 LHS = 2x - y and RHS = 6 

(1)   Substituting x = 3  and y = 0  in 2x - y = 6 , we get

       LHS = 2× 3 -0 = 6 - 0 = 6  = RHS

       So, x = 3, y = 0  or (3. 0) is  a solution of 2x - y = 6

(2)  Substituting  x  = 0  and  y = 6 in 2x - y . we get 

       LHS = 2 × 0 - 6 = -6 ≠ RHS 

        So, (0,6) is not a solution of the equation 2x - y = 6 

(3 )  Substituting x = 2 , y =-2 in 2x - y = 6 , we get 

        LHS = 2 × 2 (-2) = 4 + 2 = 6 = RHS 

         So ( 2 ,-2) is a sloution of 2x - y = 6 

(4)   Substituting `x = sqrt3`  and y = 0  in 2x - y = 6, We get 

         LHS `2 ×  sqrt3-0 = 2sqrt3  ≠ RHS` 

         So. (`sqrt 3, 0` ) is not a solution of the equation 2x - y = 6 

(5) Substituting `x =1/2` and y = -5 in 2x -y = 6 , We get 

       LHS = `2 xx 1/2 - (-5)`= 1 + 5 = 6 RHS

         So . `(1/2, - 5  )` is a solution of the 2x - y = 6