# Simultaneous linear equation activity

From Karnataka Open Educational Resources

## Contents

### Objectives

- Students will be able to understand the meaning of consistent and inconsistent simultaneous equation.
- Students will be able to understand three conditions of consistency of simultaneous linear equations.
- Students are being identify the type of solution for a given pair of linear equations.
- Students are being identify the solution of a given pair of linear equations by using graphical method.

### Estimated Time

40 minutes

### Prerequisites/Instructions, prior preparations, if any

Students should know about Equations and Linear equations,Simultaneous linear equations

### Materials/ Resources needed

Non-digital: Graph sheet,Pencil,Ruler

Digital : Click here to open the file

### Process (How to do the activity)

Download this geogebra file from this link.

**Activity:**

Students will set the value for a1,a2 , b1,b2 and c1,c2 in slider for the line equations of the type a1x+b1y=c1 and a2x+b2y=c2 and it takes as an input and compute the value of a1/a2 , b1/b2 and c1/c2.

- If a1/a2≠b1/b2 ,then two lines meet at one unique point and obtained equations are consistent(As we are getting one point common in both the lines hence it is the only solution of pair of simultaneous linear equations).
- If a1/a2=b1/b2=c1/c2 ,then two lines disappear and become one line only and equations are consistent(one line is covering the second line so we claim that lines are coincident and meet at infinitely many point,it means number of solutions are infinitely many).
- If a1/a2=b1/b2≠c1/c2 ,then two lines are parallel they never meet at any point on the plane and the equations are inconsistent(No point common in both the equations hence we can say that there is no solution of this system of equations).

### Evaluation at the end of the activity:

Complete the table with correct answers

Equation1 | Equation2 | Solution for the given equations | Type of solution | Given equations are consistent or inconsistent |
---|---|---|---|---|

x+y=12 | x-y=2 | |||

3x+2y=36 | 5x+4y=64 | |||

3x+2y=18 | 4x+5y=25 |

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