Check which of the following are solutions of the equation 2x – y =

1.	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)
Answer» (i) Check for (3, 0) Put x = 3 and y = 0 in equation 2x – y = 6 2(3) – (0) = 6 6 = 6 True statement. (3,0) is a solution of 2x – y = 6. (ii) Check for (0, 6) Put x = 0 and y = 6 in 2x – y = 6 2 x 0 – 6 = 6 -6 = 6 False statement. ⇒ (0, 6) is not a solution of 2x – y = 6. (iii) Check for (2, -2) Put x = 0 and y = 6 in 2x – y = 6 2 x 2 – (-2) = 6 4 + 2 = 6 6 = 6 True statement. ⇒ (2,-2) is a solution of 2x – y = 6. (iv) Check for (√3, 0) Put x = √3 and y = 0 in 2x – y = 6 2 x √3 – 0 = 6 2√3 = 6 False statement. ⇒(√3, 0) is not a solution of 2x – y = 6. (v) Check for (1/2, -5) Put x = 1/2 and y = -5 in 2x – y = 6 2 x (1/2) – (-5) = 6 1 + 5 = 6 6 = 6 True statement. ⇒ (1/2, -5) is a solution of 2x – y = 6.

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)

Answer»

(i) Check for (3, 0)

Put x = 3 and y = 0 in equation 2x – y = 6

2(3) – (0) = 6

6 = 6

True statement.

(3,0) is a solution of 2x – y = 6.

(ii) Check for (0, 6)

Put x = 0 and y = 6 in 2x – y = 6

2 x 0 – 6 = 6 -6 = 6

False statement.

⇒ (0, 6) is not a solution of 2x – y = 6.

(iii) Check for (2, -2)

Put x = 0 and y = 6 in 2x – y = 6

2 x 2 – (-2) = 6

4 + 2 = 6

6 = 6

True statement.

⇒ (2,-2) is a solution of 2x – y = 6.

(iv) Check for (√3, 0)

Put x = √3 and y = 0 in 2x – y = 6

2 x √3 – 0 = 6

2√3 = 6

False statement.

⇒(√3, 0) is not a solution of 2x – y = 6.

(v) Check for (1/2, -5)

Put x = 1/2 and y = -5 in 2x – y = 6

2 x (1/2) – (-5) = 6

1 + 5 = 6

6 = 6

True statement.

⇒ (1/2, -5) is a solution of 2x – y = 6.