How to solve simultaneous equations using graphs

How to solve simultaneous equations using graphs.

How much is each ticket?

Draw a bar to represent one adult and two children’s tickets.

Let’s call the adult ticket 𝑦 and the child ticket 𝑥.

Another bar represents the total of £7.

Do the same for the second set of tickets.

And simplify the diagram by writing 2𝑥.

And on the other, 5𝑥.

You can see that 𝑦 + 2 = 7.

Which means 𝑦 = 7 – 2𝑥.

You can also rewrite the second equation, 𝑦 = 13 – 5𝑥.

Now, draw their graphs.

First, draw a table of values.

Start with 𝑥 = 0 and substitute this into our equation.

When 𝑥 = 0, 𝑦 = 7.

Next, substitute 𝑥 = 1.

𝑦 = 5.

Substitute up until 𝑥 = 4.

We need to do the same again for the equation, 𝑦 = 13 – 5𝑥, with a new table of values and substitute 𝑥 = 0.

𝑥 = 1.

𝑥 = 2.

𝑥 = 3.

And, finally, 𝑥 = 4.

You now have five pairs of co-ordinates for both line graphs and you need to plot them both on the same axes.

Draw the 𝑥 and 𝑦 axes. Make sure the 𝑥-axis includes the values 0 to 4, and the 𝑦-axis the values –7 to 13.

Plot the co-ordinates on the axes. Remember, the 𝑥 co-ordinate is always first.

We’ve plotted the points from the first table. Join these points with a straight line.

𝑦 = 7 – 2𝑥.

Now, plot the co-ordinates from our second table. Join these points with a straight line.

𝑦 = 13 – 5𝑥.

Both lines cross each other at one co-ordinate: when 𝑥 = 2 and when 𝑦 = 3.

This means our 𝑥 value is 2 and our 𝑦 value is 3.

So, the adult ticket, 𝑦, is £3.

And the child ticket, 𝑥, is £2.