Solving Simultaneous Solving Simultaneous Linear EquationsLinear Equations

Using Puzzles to Engage PupilsUsing Puzzles to Engage Pupils

( Algebra Balance Concept) ( Algebra Balance Concept)

Objective of Puzzles :-

• Engage Pupils in Interesting Activities• Reinforce concept of equation as a

balance• Use visual puzzles to demonstrate

substitution and elimination concepts

Puzzles Puzzles

Puzzles Puzzles

What should be on the left of the scale ?

Puzzle extracted from Mensa Mind Workout, Josephine Fulton, Carlton Books Ltd, 1999.

Explanation of Puzzles Explanation of Puzzles

2 B = 2 X 3A = 6 A

So C = 6A

B + C = 2 X 3A = 6 A

So B + C = 3A + 6A = 9A

Use Substitution Concept to equate symbols

B = 3A

Answer : B & C is balanced by 9 As

Puzzle extracted from Mensa Mind Workout, Josephine Fulton, Carlton Books Ltd, 1999.

PuzzlesPuzzles

Puzzle extracted from Mensa Mind Workout, Josephine Fulton, Carlton Books Ltd, 1999.

Explanation of PuzzlesExplanation of Puzzles

Take away the symbols (on both sides of the balance) shown on the top left balance from the top right balance.

The remaining 2 pentagons is balanced by 1 up-arrow.

Answer 2 pentagons is balanced by 1 up-arrow

We used “Elimination” - take away other symbols, leaving the ones we need

Puzzle extracted from Mensa Mind Workout, Josephine Fulton, Carlton Books Ltd, 1999.

PuzzlesPuzzles

Puzzle extracted from Mensa Mind Workout, Josephine Fulton, Carlton Books Ltd, 1999.

PuzzlesPuzzles

2 Clouds - 2x

1 Sun - y

7 birds - 7 units

2x + y 7

1 Cloud - x

1 Sun - y

5 birds - 5 units

x + y 5

3 Clouds - 3 x

? birds - ? units

3x ?

PuzzlesPuzzles

2x + y = 7 ……. Eqn 1

x + y = 5 ……….Eqn 2

So 3x = 3 × 2 = 6

Answer : 3 clouds have 6 birds

By Elimination ie. Take away the sun, cloud and 5 birds in Picture 2 from Picture 1

Eqn 1 - Eqn 2 :

x = 2 ……….Eqn 3

(1 cloud - 2 birds )

Puzzle extracted from Mensa Mind Workout, Josephine Fulton, Carlton Books Ltd, 1999.

Solving Simultaneous Solving Simultaneous Linear EquationsLinear Equations

•Text Book Problems Text Book Problems

Work out examples fromWork out examples from•Ex 8A - Ex 8A - •Ex 8B -Ex 8B -•Ex 8C -Ex 8C -

Solving Simultaneous Solving Simultaneous Linear EquationsLinear Equations

• Balance the EquationsBalance the Equations

• ‘ ‘Reduce’ and Solve - Use eitherReduce’ and Solve - Use either–Substitution or –Elimination

• Relevant answers for word problems !Relevant answers for word problems !

Pointers to Remember :Pointers to Remember :