Simultaneous Equations

L.O To be able to solve equations with 2 different variables by satisfying both equations in the problem

When we looked at Linear Equations we were simply working the value of the term in the problem. Notice they were all something like 4p + 10 = 5p – 2 both containing “p” so we could easily solve the problem. What if you received a problem like 4x + y = 15 & 2x + 3y = 10 . How would you tackle this when you would still have the variables “x” and “y” left at the end? This is where simultaneous equations come in.

Example 1: Solve the simultaneous equations

Example 2 : Solve the simultaneous equations

Example 3 : Solve the simultaneous equations

Example 4 : Solve the simultaneous equations

Writing Simultaneous Equations

In many problems you will also have to write out the simultaneous equations out themselves. These can be more challenging at the start but is simply algebraic equations with a context.

Word Problems

a) Alison goes stationary shopping before university. She buys 7 sharpeners and 4 rubbers that cost her £5.00, and then she buys 3 sharpeners and 2 rubbers that cost her £2.00. Work out the cost of a sharpener and rubber each and calculate how much it would be to buy 5 sharpeners and 6 rubbers.

b) Billy is going to university and is taking large boxes (x) and small boxes (y) . He wants to know if they will all fit on his wall. When he takes away the length of a small box from a large box he gets 2m. However when he stacks 2 large boxes and 1 small box he gets a total of 10m. Work out the length of a small box and a large box and how many of each he could fit on an 8 m wall.

He can fit 4 small boxes and 2 large boxes

c) Ellie is collecting stamps and coins. She places them all on a page in her book. She rearranges one of the lines by taking off 2 coins, so she is only left with 6 stamps which comes to a total of 33 cm. On another line she places 4 stamps and 3 coins ; and this comes to 9 cm. Work out the theoretical length of a stamp and a coin. If the length of a page in her book is 50 cm how many of stamps could she stick on the page.

She can fit 11 stamps

c)Mark is playing video games. His characters is collecting gold and silver which his character sells for money. On level 1 he sold 4 gold coins and 3 silver coins for 3 dollars. On level 2 however he sold 6 gold coins and 5 silver coins for 7 dollars. Work out the gamin value of each silver coin and gold coin. How much can he earn if on level 3 he gains 3 gold coins and 6 silver coins?

27 dollars