A Strand 4 Unit 5 Band h
Practising skills
1 a Write down the co-ordinates of the point
of intersection of the 2 lines on this graph.
b Write down the solution of these simultaneous
equations.
x+y=4
y=x–2
c Check your answer by substituting values for
x and y in the 2 equations.
2 a Write down the co-ordinates of the point
of intersection of the 2 lines on this graph.
b Solve these simultaneous equations in 2 ways.
y = 4x – 3
4y = 3x + 1
i By looking at the graph.
ii By algebra, using the substitution method.
y
6
5
4
3
2
1
y=x–2
0
−6 −5 −4 −3 −2 −1
−1
−2
−3
−4
−5
−6
1 2 3 4 5 6
x+y=4
y
y = 4x – 3
6
5
4
3
2
1
4y = 3x + 1
0
−6 −5 −4 −3 −2 −1
−1
−2
−3
−4
−5
−6
3 a One of the lines on this graph is y =
other is 3y = 4x – 1. Which is which?
x and the
b Write down the co-ordinates of the point of
intersection of the 2 lines.
c Solve these simultaneous equations.
y=x
3y = 4x – 1
i By looking at the graph.
ii By algebra, using the substitution method.
© Hodder & Stoughton Ltd 2015
x
y
6
5
4
3
2
1
0
−6 −5 −4 −3 −2 −1
−1
−2
−3
−4
−5
−6
1 2 3 4 5 6
x
e
m
1 2 3 4 5 6
x
1
A Strand 4 Unit 5 Band h
y
4 a One of the lines on this graph has equation
y = 1 x + 12.
3
3
The other has equation y = – 1 x + 2 1 .
2
2
Which is which?
e
b Write down the co-ordinates of the point of
intersection of the 2 lines.
c Write down the 2 simultaneous equations for
which this point is the solution.
d Check your solution by substituting your x- and
y-values in both equations.
6
5
4
3
2
1
0
−6 −5 −4 −3 −2 −1
−1
−2
−3
−4
−5
−6
m
1 2 3 4 5 6
5 a Copy and complete this table of values for y = 3x – 2.
x
3x
0
–2
–2
y = 3x – 2
–2
1
2
3
0
b Make a table of values for the line y = 6 – x.
c Draw the lines y = 3x – 2 and y = 6 –
d
x on the same graph.
Use your graph to solve the simultaneous equations y = 3x – 2 and y = 6 – x.
e Use algebra to check your solution.
6 a Draw the lines y = x + 3 and y = 1 x + 2 1 on the same graph.
4
4
b Use your graph to solve the simultaneous equations y = x + 3 and 4y = x + 9.
7 a Copy and complete this table of values for y = 8 – x.
x
y=8–x
0
1
2
3
8
b Make a table of values for the line y = x + 4.
c Draw the lines y = 8 – x and y = x + 4 on the same graph.
d Use your graph to solve the simultaneous equations y = 8 – x and y = x + 4.
e Check your answer using algebra to solve the equations.
8 a Draw the lines y = 3x – 1 and y = x – 1 on the same graph.
b Use your graph to solve the simultaneous equations y = 3x – 1 and y = x – 1.
c Use algebra to check your answer.
2
© Hodder & Stoughton Ltd 2015
x