# Class 10 Maths - Lab Activity - Linear Equations

Objective

To verify the conditions for consistency of a system of linear equations in two variables by graphical representation.

Prerequisite Knowledge

1. Plotting of points on a graph paper.

2. Condition of consistency of lines parallel, intersecting, coincident,

Materials Required

Graph papers, fevicol, geometry box, cardboard.

Procedure

Consider the three pairs of linear equations

1st pair:

2x-5y+4=0,

2x+y-8 = 0

2nd pair:

4x + 6y = 24,

2x + 3y =6

3rd pair:

x-2y=5,

3x-6y=15

1. Take the 1st pair of linear equations in two variables, e.g., 2x – 5y +4=0, 2x +y- 8 = 0.

2. Obtain a table of at least three such pairs (x, y) which satisfy the given equations.

3. Plot the points of two equations on the graph paper as shown below.

4. Observe whether the lines are intersecting, parallel or coincident. Write the values in observation table.
Also, check for:
```   a₁         b₁         c₁
---- = ---- = ----
a₂         b₂         c₂

```
5. Take the second pair of linear equations in two variables

6. Repeat the steps 3 and 4 and draw linear graph as shown.

7. Take the third pair of linear equations in two variables,i.e. x-2y=5, 3x-6y=15. Plot XY values.

8. Repeat steps 3 and 4 and plot the graph (as shown)

Observation:
Following are the observations:

1. In 1st pair, for intersecting lines

```   a₁         b₁
---- ≠ ----
a₂         b₂
```

2. For second pair (parallel lines)
```   a₁         b₁         c₁
---- = ---- ≠ ----
a₂         b₂         c₂

```

3. For 3rd pair of equations (coincident lines)
```   a₁         b₁         c₁
---- = ---- = ----
a₂         b₂         c₂
```

Result
The conditions for consistency of a system of linear equations in two variables is verified.