Given the linear equation `2x+ 3y- 8= 0`, write another linear equation in two variables such that the geometrical representation of the pair so formed is
coincident lines

Answer

To find another linear equation in two variables such that the geometrical representation of the pair formed is coincident lines, we can follow these steps:

### Step 1: Identify the given linear equation
The given linear equation is:
\[ 2x + 3y - 8 = 0 \]

### Step 2: Rewrite the equation in standard form
In standard form, the equation can be expressed as:
\[ A_1x + B_1y + C_1 = 0 \]
where \( A_1 = 2 \), \( B_1 = 3 \), and \( C_1 = -8 \).

### Step 3: Understand the condition for coincident lines
For two lines to be coincident, the ratios of the coefficients must be equal:
\[ \frac{A_1}{A_2} = \frac{B_1}{B_2} = \frac{C_1}{C_2} \]
where \( A_2, B_2, C_2 \) are the coefficients of the second equation.

### Step 4: Choose a ratio for the second equation
Let's assume:
\[ \frac{A_2}{A_1} = k \quad \text{(where \( k \) is a constant)} \]
We can choose \( k = 2 \) for simplicity. Therefore:
\[ A_2 = 2 \times 2 = 4 \]
\[ B_2 = 2 \times 3 = 6 \]
\[ C_2 = 2 \times (-8) = -16 \]

### Step 5: Write the new linear equation
Now, we can write the new linear equation using these coefficients:
\[ 4x + 6y - 16 = 0 \]

### Step 6: Conclusion
Thus, the second linear equation that represents coincident lines with the given equation is:
\[ 4x + 6y - 16 = 0 \]