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

We are given the equation: \( x - 2y = 4 \)

1. For \( (0, 2) \):

Substitute \( x = 0 \) and \( y = 2 \) into the equation:

\[ 0 - 2(2) = 0 - 4 = -4 \neq 4 \]

Hence, \( (0, 2) \) is not a solution.

2. For \( (2, 0) \):

Substitute \( x = 2 \) and \( y = 0 \) into the equation:

\[ 2 - 2(0) = 2 - 0 = 2 \neq 4 \]

Hence, \( (2, 0) \) is not a solution.

3. For \( (4, 0) \):

Substitute \( x = 4 \) and \( y = 0 \) into the equation:

\[ 4 - 2(0) = 4 - 0 = 4 \]

Hence, \( (4, 0) \) is a solution.

4. For \( \left( \frac{2}{2}, \frac{4}{2} \right) = (1, 2) \):

Substitute \( x = 1 \) and \( y = 2 \) into the equation:

\[ 1 - 2(2) = 1 - 4 = -3 \neq 4 \]

Hence, \( (1, 2) \) is not a solution.

5. For \( (1, 1) \):

Substitute \( x = 1 \) and \( y = 1 \) into the equation:

\[ 1 - 2(1) = 1 - 2 = -1 \neq 4 \]

Hence, \( (1, 1) \) is not a solution.