**Solving Two Linear Equations in Two Variables and Representing it in a Graph**

To solve a system of two linear equations in two variables, we need to find the values of the variables that satisfy both equations simultaneously. This can be done using various methods, including the substitution method, elimination method, or graphing method. In this guide, we will focus on the graphing method and explain the steps involved in solving such a system and representing it on a graph.

**Graphing Method:**
The graphing method involves plotting the equations on a graph to visually determine the point of intersection, which represents the solution to the system of equations.

1. **Write the Equations in Standard Form:**
- Ensure that both equations are in standard form, which is Ax + By = C, where A, B, and C are constants.
- For example, consider the following system of equations:
Equation 1: 2x + 3y = 6
Equation 2: -4x + 5y = 10

2. **Plotting the Equations on a Graph:**
- Convert each equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
- Equation 1: 2x + 3y = 6
Rewrite as: 3y = -2x + 6
Divide by 3: y = -2/3x + 2
- Equation 2: -4x + 5y = 10
Rewrite as: 5y = 4x + 10
Divide by 5: y = 4/5x + 2
- Plot the two equations on the same graph using their respective slopes and y-intercepts. Choose a suitable scale for the x and y axes.

3. **Find the Point of Intersection:**
- The point where the two lines intersect represents the solution to the system of equations.
- Locate the point of intersection visually on the graph.
- In our example, the lines intersect at the coordinates (2, 0).

4. **Check the Solution:**
- Substitute the values of x and y from the point of intersection into both equations to verify if they satisfy both equations.
- For our example, substitute x = 2 and y = 0 into both equations:
Equation 1: 2(2) + 3(0) = 6 (True)
Equation 2: -4(2) + 5(0) = 10 (False)
- Since one equation is satisfied and the other is not, the point of intersection (2, 0) is not a valid solution to the system of equations.

By following these steps, you can solve a system of two linear equations in two variables using the graphing method. Remember to plot the equations accurately and locate the point of intersection precisely to obtain the correct solution.

U have to put some assume value in one weather it is x or y then u find the other value .....do this in both equations and atleast 3 times so u get the perfect answer and also to check weather the line is straight or not if not check your answer again..... plot these points on the graph ...u will get your answer