Find the value of 'a' if (1,-1) is the solution of the equation 2x+ay =5 find two more solutions of the equation

Answer

To solve the problem step by step, let's break it down into two parts: finding the value of 'a' and then finding two more solutions of the equation.

### Step 1: Finding the value of 'a'

1. **Given Equation**: The equation is \( 2x + ay = 5 \).
2. **Substituting the Solution**: We know that (1, -1) is a solution. This means when \( x = 1 \) and \( y = -1 \), the equation should hold true.
\[ 2(1) + a(-1) = 5 \]
3. **Simplifying the Equation**:
\[ 2 - a = 5 \]
4. **Isolating 'a'**: To find 'a', we rearrange the equation:
\[ -a = 5 - 2 \]
\[ -a = 3 \]
\[ a = -3 \]

### Step 2: Finding Two More Solutions

Now that we have the value of \( a \), we can rewrite the equation:
\[ 2x - 3y = 5 \]

1. **Finding the First Additional Solution**:
- Let's choose \( x = 2 \).
- Substitute \( x \) into the equation:
\[ 2(2) - 3y = 5 \]
\[ 4 - 3y = 5 \]
- Rearranging gives:
\[ -3y = 5 - 4 \]
\[ -3y = 1 \]
\[ y = -\frac{1}{3} \]
- So, one additional solution is \( (2, -\frac{1}{3}) \).

2. **Finding the Second Additional Solution**:
- Let's choose \( y = 2 \).
- Substitute \( y \) into the equation:
\[ 2x - 3(2) = 5 \]
\[ 2x - 6 = 5 \]
- Rearranging gives:
\[ 2x = 5 + 6 \]
\[ 2x = 11 \]
\[ x = \frac{11}{2} \]
- So, the second additional solution is \( \left(\frac{11}{2}, 2\right) \).

### Final Answers:
- The value of \( a \) is \( -3 \).
- The two additional solutions are \( (2, -\frac{1}{3}) \) and \( \left(\frac{11}{2}, 2\right) \).