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18.4 Simultaneous equations

2 Use this graph to solve these pairs of equations y
simultaneously. 6
1
a y = 2x + 1 and y = x − 2
2 4
1
b y = 2x + 1 and y = − x + 6
2
1
1
c y = x − 2 and y = − x + 6 2
2 2
0 x
–2 2 4 6 8 10 12
–2

–4

3 a Draw the lines with these equations. Draw all of them on the same grid.
1
i y = x − 3 ii y = 7 − x iii y = x + 1
2
b Use the graphs to solve these pairs of equations simultaneously.
1
1
i y = x − 3 and y = 7 − x ii y = x − 3 and y = x + 1 iii y = 7 − x and y = x + 1
2 2

4 Use this graph to find approximate solutions of the y
following pairs of simultaneous equations. 30
a y = 0.5x − 5 and y = −1.5x + 30
b y = 0.5x − 5 and y = −0.67x + 20 20
c y = −0.67x + 20 and y = −1.5x + 30
y = 0.5x – 5
10
The solutions are approximate because
you are reading them from a graph.
–10 0 10 20 30 40 x

–10 y = –1.5x + 30 y = –0.67x + 20

5 Look at these two simultaneous equations. 1

Draw graphs to find approximate solutions. y = 3x − 2 y = x + 4
3
6 Look at these two simultaneous equations. 1 5

Draw graphs to find approximate solutions. y = x − 3 y = − x + 6
2
2
7 a Write the equation 3x + 2y = 12 in the form y = mx + c. y
b Write the equation x + 3y + 3 = 0 in the form y = mx + c. 6
c Use this graph to solve the equations 3x + 2y = 12 and
x + 3y + 3 = 0 simultaneously. 4

2

0 x
–4 –2 2 4 6
–2

–4

172 18 Graphs 18 Graphs