Check which of the following are solutions of the equation 2x - y = 6 and Which are not:
(i) (3, 0)
(ii) (0, 6)
(iii) (2, - 2)
(iv) (√3, 0)
(v) (1/2 , - 5)
We are given, 2x - y = 6
(i) In the equation 2x - y = 6,
We have L.H.S = 2x - y and R.H.S = 6
Substituting x = 3 and y = 0 in 2x - y,
We get L.H.S = 2 × 3 - 0 = 6 ⟹ L.H.S = R.H.S
⟹ (3, 0) is a solution of 2x - y = 6.
(ii) In the equation 2x - y = 6, We have L.H.S= 2x - y and R.H.S = 6
Substituting x = 0 and y = 6 in 2x - y
We get L.H.S = 2 × 0 - 6 = - 6
⟹ L.H.S ≠ R.H.S
⟹ (0, 6) is not a solution of 2x - y = 6.
(iii) In the equation 2x - y = 6,
We have L.H.S = 2x - y and R.H.S = 6
Substituting x = 2 and y = - 2 in 2x - y,
We get L.H.S = 2 × 2 - (-2) = 6
⟹ L.H.S = R.H.S
⟹ (2, - 2) is a solution of 2x - y = 6.
(iv) In the equation 2x - y = 6,
We have L.H.S = 2x- y and R.H.S = 6
Substituting x = √3 and y = 0 in 2x - y,
We get L. H. S = 2 × √3 - 0
⟹ L.H.S ≠ R.H.S
⟹ (√3, 0) is not a solution of 2x - y = 6.
(v) In the equation 2x - y = 6,
We have L.H.S = 2x - y and R.H.S = 6
Substituting x = 1/2 and y = in 2x - y, we get L.H.S = 2 × (1/2) - (-5)
⟹ 1 + 5 = 6
⟹ L.H.S = R.H.S
⟹ (12, - 5) is a solution of 2x - y = 6.