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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.

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Find out how to solve simultaneous equations using bar models

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Click to see a step-by-step slideshow.
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YOU WILL NEED: A whiteboard, a ruler, pens and a board rubber.
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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.
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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.
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STEP 3 - Both bar models have y + 2x = 7...
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...remove these. You are left with 3x = 6.
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STEP 4 - Work out the value of x. 6 ÷ 3 is 2. So x = 2.
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STEP 5 - Now you know that y + 2x = 7 and that x = 2. So y+4 = 7.
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STEP 6 - Now work out y. If the bar totalled 7, then y must be 3. 7-4 = 3. y = 3.
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Therefore: an adult ticket costs £3 and a child ticket costs £2.

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