**Graphical Representation of the Linear Equations**

To graphically represent the pair of linear equations 8x - 5y = 9 and 16x - 10y = 27, we first need to rewrite the equations in slope-intercept form, which is y = mx + b.

The equation 8x - 5y = 9 can be rewritten as:
-5y = -8x + 9
y = (8/5)x - (9/5)

Similarly, the equation 16x - 10y = 27 can be rewritten as:
-10y = -16x + 27
y = (16/10)x - (27/10)
y = (8/5)x - (27/10)

Now, we can plot the graph of these equations on a coordinate plane.

**Plotting the Graph**

1. Determine the slope and y-intercept of the first equation:
The slope of the first equation is 8/5, and the y-intercept is -9/5.

2. Plot the y-intercept:
On the y-axis, mark a point at -9/5.

3. Find another point on the line:
To find another point, we can choose any x-value and substitute it into the equation to find the corresponding y-value. Let's choose x = 0:
y = (8/5)(0) - (9/5)
y = -9/5

So, we have another point at (0, -9/5).

4. Plot the points and draw a line:
Using the two points we found, plot them on the coordinate plane and draw a line passing through them. This line represents the first equation.

5. Repeat steps 1-4 for the second equation:
The slope of the second equation is also 8/5, but the y-intercept is -27/10.

- Plot the y-intercept:
On the y-axis, mark a point at -27/10.

- Find another point on the line:
Let's choose x = 0:
y = (8/5)(0) - (27/10)
y = -27/10

So, we have another point at (0, -27/10).

- Plot the points and draw a line:
Using the two points we found, plot them on the coordinate plane and draw a line passing through them. This line represents the second equation.

**Analyzing the Graph**

Now that we have plotted the two lines representing the equations, we can analyze their intersection point.

In this case, the two lines are parallel and will never intersect. Therefore, there is no solution to the given pair of linear equations.

This can be seen visually on the graph as the lines do not intersect at any point. The absence of an intersection point indicates that there is no common solution to the pair of equations.

Hence, the pair of linear equations 8x - 5y = 9 and 16x - 10y = 27 has no solution.

Given equations - 8x 5y=9 , 16x 10y=27
Now,
a1: a2 = b1:b2 = c1:c2. So,
putting values of a1, a2 ,b1, b2 ,c1,c2
a1=8
a2=16
b1=5
b2=10
c1=9
c2=27
according to the question,
8 : 16= 1: 2
5 : 10= 1 :2
9 : 27= 1: 3

So, [a1:a2 is equal to b1:b2 is not equal to c1:c2]
Hence it is no solution.

Now, show it graphically on graph paper and the lines formed will be parallel to each other.

Remember this sign ( : ) has been used as division.

thank u.... hope it will help you.....