Simultaneous Equations Forming Demonstration This resource provides animated

Simultaneous Equations – Forming – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

Joe buys an apple & a banana for 90 p. How much does a banana cost? This is an equation we can try to solve, but we have 2 variables & no other information. The variables can have a range of values & we can’t solve the equation!

Joe buys an apple & a banana for 90 p. How much does a banana cost? Geeta buys 2 apples for 80 p. How can we combine this information to find the price of each item (the value of each variable)?

In a supermarket, 2 apples & a banana cost £ 1 1 apple & 1 banana cost 70 p. The difference in items is 1 apple. The difference in price is 30 p. How can we find the price of each? We can calculate the difference between the two equations.

To solve simultaneous equations we compare them to find the difference. £ 2. 50 £ 1. 50 The difference in items is 1 burger. The difference in price is £ 1 (100).

To solve simultaneous equations we compare them to find the difference. £ 2 £ 1. 40 The difference in items is 1 burger. The difference in price is 60 p.

To solve simultaneous equations we compare them to find the difference. £ 2. 50 £ 2. 90 The difference in items is 1 fries. The difference in price is 40 p.

Elimination Method 50 p Substitute the value of one strawberry to find the value of one banana. 50 p

Elimination Method £ 2 Substitute the value of one burger to find the value of one fries. £ 2

In 6 different shops two orders are placed. Compare the orders (calculate the differences) to find the price of each item. 30 50 25 60 £ 1. 10 85 p £ 1. 70 80 p £ 1. 10 50 p 90 p £ 1. 80 £ 1. 40 £ 3. 70 £ 3. 40 Harry buys 3 loaves of bread & 4 chocolate bars for £ 4. 50 Barry buys 7 loaves of bread & 4 chocolate bars and pays £ 7. 30 £ 5. 50 L = 70 p Kimmy buys 2 teas & 2 coffees and pays £ 2. 60 T = 55 p C = 60 p Timmy buys 4 teas & 5 coffees for £ 5. 95 C = 75 p

How can we form a pair of simultaneous equations from this information? Julie went to the shop – it was a Thursday – and picked up 3 packets of biscuits. Before she left the store she saw that loaves of bread were a good price and so she bought 4. She paid with a £ 10 note and got £ 5. 80 change Total spent on goods = 420 80 p 45 p Kirk had £ 5 to spend at the store. He knew he needed a couple of loaves of bread so he picked them up first. He thought about buying some luxury biscuits but he wanted quantity, not quality! Instead he bought 3 packets of cheap sugary biscuits. After putting a quid in the charity box he left the store with 70 p. Total spent on goods = 330

At a takeout… 3 tacos & 1 slice of pizza costs £ 2 1 taco & 1 slice of pizza costs £ 1. 20 = £ 2 = £ 1. 20 1) Subtract to find the difference. 2) Solve to find the value of 1 variable. 3) Substitute & solve to find the remaining value. 4) Substitute & check!

At a takeout… 4 coffees & 1 doughnut costs £ 4. 10 1 coffee & 1 doughnut costs £ 1. 40 = £ 4. 10 = £ 1. 40 1) Subtract to find the difference. 2) Solve to find the value of 1 variable. 3) Substitute & solve to find the remaining value. 4) Substitute & check!

At a takeout… 3 fries & 2 sandwiches cost £ 4. 80 1 fries & 2 sandwiches cost £ 3. 20 = £ 4. 80 = £ 3. 20 1) Subtract to find the difference. 2) Solve to find the value of 1 variable. 3) Substitute & solve to find the remaining value. 4) Substitute & check!

At a takeout… 2 teas & 4 ice creams cost £ 3. 80 2 teas & 2 ice creams cost £ 2. 60 = £ 3. 80 = £ 2. 60 1) Subtract to find the difference. 2) Solve to find the value of 1 variable. 3) Substitute & solve to find the remaining value. 4) Substitute & check!

At a takeout… 5 cookies & 5 juices cost £ 6. 50 2 cookies & 5 juices cost £ 5. 30 1) Subtract to find the difference. 2) Solve to find the value of 1 variable. 3) Substitute & solve to find the remaining value. 4) Substitute & check!

At a takeout… 6 loaves & 10 rolls cost £ 11. 80 6 loaves & 6 rolls cost £ 9. 00 1) Subtract to find the difference. 2) Solve to find the value of 1 variable. 3) Substitute & solve to find the remaining value. 4) Substitute & check!

= £ 1. 60 = 50 p × 2 = £ 1 20 p 30 p What is the problem with finding the difference? If we subtract we still have 2 variables in the equation. Before we subtract, we can convert the first equation into an equivalent equation & balance coefficients.

Find the value of each item. A B 15 p 90 p = £ 2. 70 60 p = £ 1. 30 35 p = £ 1. 50 = 85 p 1) Subtract to find the difference. C 2) Solve to find the value of 1 variable. It costs £ 11. 90 for 7 sodas and 3 hotdogs. 1 hotdogs = £ 1. 40 1 soda = £ 1. 10 D Anna is sent to the shop for the office lunch. She has a £ 20 note and buys 4 sandwiches and 4 apples. She gets £ 7. 60 in change. The next day Jay is sent. He has to buy 2 extra sandwiches and also a chocolate bar (90 p) for his boss. He pays £ 18. 10 3) Substitute & solve to find the remaining value. 4) Substitute & check! 1 sandwich = £ 2. 40 1 apple = 70 p 3 hotdogs and 5 sodas cost £ 9. 70

Find the value of each item. A B 57 p = £ 3. 03 82 p 52 p = £ 3. 42 67 p = £ 1. 39 = £ 1. 86 1) Subtract to find the difference. C 2) Solve to find the value of 1 variable. It costs £ 16. 92 for 4 sodas and 9 slices of pizza. 1 slice of pizza = £ 1. 44 1 soda = 99 p D Mack is sent to the shop for the office lunch. He has a £ 20 note and buys 5 sandwiches and 5 drinks. He gets £ 2. 25 in change. The next day Igor is sent. He has to buy 3 extra sandwiches & he pays £ 24. 80 3) Substitute & solve to find the remaining value. 4) Substitute & check! 1 sandwich = £ 2. 35 1 drink = £ 1. 20 5 slices of pizza and 4 sodas cost £ 11. 16

Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths. co. uk