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The image contains a system of linear equations in Bengali. Let's analyze the problem step by step.

The system of equations is:

\[
2x + 3y + 5 = 0
\]
and
\[
4x - 6y - 7 = 0
\]

We are asked to find the point of intersection of these two lines, specifically checking if the point \((1, 2)\) lies on the lines, and then solve the system of equations.

### Steps to solve:

1. **Rewrite the system of equations:**
   \[
   2x + 3y + 5 = 0 \quad \text{(Equation 1)}
   \]
   \[
   4x - 6y - 7 = 0 \quad \text{(Equation 2)}
   \]

2. **Simplify or eliminate variables:**
   Multiply the first equation by 2 so the coefficients of \(x\) in both equations are the same:
   \[
   2(2x + 3y + 5) = 4x + 6y + 10 = 0 \quad \text{(Equation 1 multiplied by 2)}
   \]
   Now we have:
   \[
   4x + 6y + 10 = 0 \quad \text{(Equation 1')}
   \]
   and
   \[
   4x - 6y - 7 = 0 \quad \text{(Equation 2)}
   \]

3. **Add the two equations to eliminate \(x\):**
   \[
   (4x + 6y + 10) + (4x - 6y - 7) = 0
   \]
   Simplifying:
   \[
   8x + 3 = 0
   \]
   Therefore, 
   \[
   8x = -3 \quad \Rightarrow \quad x = -\frac{3}{8}
   \]

4. **Substitute the value of \(x\) back into one of the original equations (say Equation 1):**
   \[
   2x + 3y + 5 = 0
   \]
   Substituting \(x = -\frac{3}{8}\):
   \[
   2\left(-\frac{3}{8}\right) + 3y + 5 = 0
   \]
   Simplifying:
   \[
   -\frac{6}{8} + 3y + 5 = 0 \quad \Rightarrow \quad -\frac{3}{4} + 3y + 5 = 0
   \]
   Multiply everything by 4 to eliminate fractions:
   \[
   -3 + 12y + 20 = 0 \quad \Rightarrow \quad 12y + 17 = 0
   \]
   Therefore,
   \[
   12y = -17 \quad \Rightarrow \quad y = -\frac{17}{12}
   \]

### Conclusion:
The solution to the system of equations is:
\[
x = -\frac{3}{8}, \quad y = -\frac{17}{12}
\]
Thus, the point \((- \frac{3}{8}, - \frac{17}{12})\) is the solution of the system.

Would you like more details on any of these steps or further explanations?

---

Here are 5 related questions to deepen understanding:
1. How can we verify that a given point lies on both lines?
2. What are other methods to solve systems of linear equations besides elimination?
3. How do we interpret the graphical meaning of solving two linear equations?
4. What is the condition for two lines to be parallel or intersecting?
5. How does the substitution method differ from the elimination method in solving systems of equations?

**Tip**: Always check your solution by substituting the values of \(x\) and \(y\) into both original equations to ensure they hold true.

Solve the system of linear equations: 2x + 3y + 5 = 0 and 4x - 6y - 7 = 0. Determine if the point (1, 2) lies on the lines.

Learn how to solve the system of linear equations 2x + 3y + 5 = 0 and 4x - 6y - 7 = 0 using the elimination method. Includes step-by-step calculations and verification if point (1, 2) lies on the lines. Suitable for students in Grades 9-12.

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