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18.4 Simultaneous equations

18.4 Simultaneous equations

Here is a pair of equations. y = 0.5x + 4 y = 2.5x − 3
In Unit 13 you learnt how to use algebra to solve these simultaneously.

You can write: 0.5x + 4 = 2.5x − 3
Subtract 0.5x from both sides: 4 = 2x − 3
Add 3 to both sides: 7 = 2x
Divide both sides by 2: x = 3.5
Find y by substitution: y = 0.5x + 4 = 0.5 × 3.5 + 4 = 5.75

You can also use a graph to solve equations like these.

Worked example 18.4
a Draw a graph of the lines with equations y = 0.5x + 4 and y = 2.5x − 3.
b Use your graph to solve the equations y = 0.5x + 4 and y = 2.5x − 3 simultaneously.

a y Start with a table of values
8 Choose at least three values for x.
6
x 0 2 4
4
0.5x + 4 4 5 6
2
2.5x − 3 −3 2 7
0 x
–4 –2 2 4 6 8
–2
–4

b The lines cross at approximately (3.5, 5.8).
The approximate solution is x = 3.5 and y = 5.8.
The solution may not be exact because it is
based on a graph.

) Exercise 18.4

1 The graph shows the lines with equations y = 2x − 2, y
y = x − 4 and y + x = 4. 4
Use the graph to solve these pairs of equations simultaneously.
a y = 2x − 2 and y = x − 4 2
b y = 2x − 2 and y + x = 4
c y = x − 4 and y + x = 4 0 x
–4 –2 2 4 6

–2

–4

–6

18 Graphs 18 Graphs 171