Find two solution sof each of the following:
(i)x+y=6 , (ii) 2x+3y=12

Answer

To find two solutions for each of the given equations, we will follow these steps:

### Part (i): Solve the equation \( x + y = 6 \)

1. **Choose a value for \( y \)**:
Let's start by choosing \( y = 1 \).

2. **Substitute \( y \) into the equation**:
\[ x + 1 = 6 \]

3. **Solve for \( x \)**:
\[ x = 6 - 1 = 5 \]
So, one solution is \( (5, 1) \).

4. **Choose another value for \( y \)**:
Now, let's choose \( y = 2 \).

5. **Substitute \( y \) into the equation**:
\[ x + 2 = 6 \]

6. **Solve for \( x \)**:
\[ x = 6 - 2 = 4 \]
So, the second solution is \( (4, 2) \).

### Summary of solutions for Part (i):
The two solutions for the equation \( x + y = 6 \) are:
1. \( (5, 1) \)
2. \( (4, 2) \)

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### Part (ii): Solve the equation \( 2x + 3y = 12 \)

1. **Choose a value for \( y \)**:
Let's start by choosing \( y = 0 \).

2. **Substitute \( y \) into the equation**:
\[ 2x + 3(0) = 12 \]
This simplifies to:
\[ 2x = 12 \]

3. **Solve for \( x \)**:
\[ x = \frac{12}{2} = 6 \]
So, one solution is \( (6, 0) \).

4. **Choose another value for \( y \)**:
Now, let's choose \( y = 2 \).

5. **Substitute \( y \) into the equation**:
\[ 2x + 3(2) = 12 \]
This simplifies to:
\[ 2x + 6 = 12 \]

6. **Solve for \( x \)**:
\[ 2x = 12 - 6 = 6 \]
\[ x = \frac{6}{2} = 3 \]
So, the second solution is \( (3, 2) \).

### Summary of solutions for Part (ii):
The two solutions for the equation \( 2x + 3y = 12 \) are:
1. \( (6, 0) \)
2. \( (3, 2) \)

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