Question

Check which of the following are solutions of the equation x – 2y = 4 and which are not: 

(i) (0, 2) 

(ii) (2, 0) 

(iii) (4, 0) 

(iv) \((\sqrt 2 , 4 \sqrt2) \)

(v) (1, 1)

Answer 1

(i) (0, 2) 

Putting x = 0 and y = 2 in the L.H.S of the given equation, 

x − 2y = 0 − 2× − 4 ≠ 4 2 

= L.H.S ≠ R.H.S 

Therefore, (0, 2) is not a solution of this equation. 

(ii) (2, 0) 

Putting x = 2 and y = 0 in the L.H.S of the given equation, 

x − 2y 2 − 2 × 0 = 2 ≠ 4 

= L.H.S ≠ R.H.S

Therefore, (2, 0) is not a solution of this equation. 

(iii) (4, 0) 

Putting x = 4 and y = 0 in the L.H.S of the given equation, 

x − 2y = 4 − 2(0) 

= 4 = R.H.S 

Therefore, (4, 0) is a solution of this equation.

(iv) \(\sqrt2,4\sqrt2\)

=\(\sqrt2-8\sqrt2=-7\sqrt2 ≠4\)

=L.H.S ≠ R.H.S

Therefore \(\sqrt2,4\sqrt2\)  is not a solution of this equation. 

(v) (1, 1) 

Putting x = 1 and y = 1 in the L.H.S of the given equation, 

x − 2y 1 − 2(1) = 1 − 2 = − 1 ≠ 4 

= L.H.S ≠ R.H.S 

Therefore, (1, 1) is not a solution of this equation.