Strand 4 Algebraic methods Unit 5 Using graphs to solve simultaneous equations Band h
Skills practice A
1 For each graph, write down the co-ordinates of the point where the lines intersect.
a
b
y
y
6
6
5
5
4
3
4
3
2
2
1
1
–3 –2 –1 0
–1
1
2
3
4
5
x
–3 –2 –1 0
–1
2
3
4
5
1
2
3
4
5
x
–2
–2
c
1
d
y
y
6
6
5
5
4
3
4
3
2
2
1
1
–3 –2 –1 0
–1
1
2
3
4
5
x
–3 –2 –1 0
–1
x
–2
–2
2 Here is a graph of the lines y = 2x + 2 and y = 5 – x.
y
6
y = 2x +2
5
4
3
2
y=5−x
1
0
1
2
3
4
5
6
x
a Write down the co-ordinates of the point where the two lines intersect.
b Write down the solution of the simultaneous equations y = 2x + 2 and y
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= 5 – x.
1
Strand 4 Algebraic methods Unit 5 Using graphs to solve simultaneous equations Band h
3 Here is a graph of the lines y
= 2x – 5 and y = x – 1.
y
5
y = 2x − 5
4
3
2 y=x−1
1
0
1
2
3
4
5
6
x
a Write down the co-ordinates of the point where the two lines intersect.
b Write down the solution of the simultaneous equations y = 2x – 5 and y
= x – 1.
4 a Copy and complete this table.
x
4x
–2
y = 4x – 2
0
0
–2
–2
1
2
3
12
–2
10
4
b Make a table for the line y = 2x + 1.
c Draw the lines y = 4x – 2 and y = 2x + 1 on the same axes.
d Use your graph to solve the simultaneous equations y = 4x –
2 and y = 2x + 1.
Reasoning
5 a Complete a table of values to find three points on these lines:
y = 2x + 3
y=6–x
y = 7 – 2x
y=x+1
b Plot each line on the same graph.
c Use your graph to solve these four pairs of simultaneous equations:
i y = 2x + 3
ii y = 6 – x
iii y = 6 – x
iv
y=x+1
y=x+1
y = 7 – 2x
y = 7 – 2x
y=x+1
d State what other pairs of equations you can solve from your graph.
Give their solutions.
2
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