��˿��

Simultaneous equations are two linear equations that can be solved using bar models.
By remembering that the same letter will always have the same value we can work out the missing values.
To solve simultaneous equations we must work out the value of x and y that make the equations work.

This video can not be played

To play this video you need to enable JavaScript in your browser.

Find out how to solve simultaneous equations using bar models

Have a go

Skip image gallery

Image caption,
Click to see a step-by-step slideshow.
Image caption,
YOU WILL NEED: A whiteboard, a ruler, pens and a board rubber.
Image caption,
STEP 1 - Look at the problem and highlight what you know. In this example you know 1 adult and 2 child tickets costs £7 and 1 adult and 5 child tickets costs £13.
Image caption,
STEP 2 - Use y to represent adult tickets and x to represent child tickets. Draw two bar models to represent the tickets sold for £7 and £13.
Image caption,
STEP 3 - Both bar models have y + 2x = 7...
Image caption,
...remove these. You are left with 3x = 6.
Image caption,
STEP 4 - Work out the value of x. 6 ÷ 3 is 2. So x = 2.
Image caption,
STEP 5 - Now you know that y + 2x = 7 and that x = 2. So y+4 = 7.
Image caption,
STEP 6 - Now work out y. If the bar totalled 7, then y must be 3. 7-4 = 3. y = 3.
Image caption,
Therefore: an adult ticket costs £3 and a child ticket costs £2.

Where next?

Discover more about this topic from Bitesize.

More on Algebra

Find out more by working through a topic

WATCH: How to solve simultaneous equations using graphs
count
15 of 29
Coordinates
count
16 of 29
WATCH: How to plot coordinates
count
17 of 29
Straight line graphs
count
18 of 29