Mathematics Year 9

1
Simultaneous equations
2
Fit the equation
3x y 20
What positive integer values of x and y satisfy
this equation?
For example, x 6 and y 2.
Can anyone think of another equation that is
satisfied by x 6 and y 2?
3
Fit the equation
3p 2q 30
What positive integer values of p and q satisfy
this equation?
For example, p 4 and q 9.
Can anyone think of another equation that is
satisfied by p 4 and q 9?
4
Fit the equation
5a 2b 24
What positive integer values of a and b satisfy
this equation?
For example, a 4 and b 2.
Can anyone think of another equation that is
satisfied by a 4 and b 2?
5
Line up
2a
b
50
The length of the line is 50. What is an
algebraic expression of this fact involving a and
b?
2a b 50
6
Line up
2a
b
50
Part of the line of length b is one unit shorter
than the part of the line of length a. What is an
algebraic expression of this fact?
b a 1
7
Line up
2a
b
50
What is an equation involving only a, that
expresses the fact that the total length is 50?
8
Line up
2a
b
50
Instead of b we can write a 1. 2a a 1
50 3a 1 50 3a 51
, so a 17
9
Line up
2a
b
50
If a 17, what is b?
b 16
10
Line up
2c
d
75
The length of the line is 75. What is an
algebraic expression of this fact involving c and
d?
2c d 75
11
Line up
2c
d
75
Part of the line of length d is 3 times as long
as a line of length c. What is an algebraic
expression of this fact?
d 3c
12
Line up
2c
d
75
What is an equation involving only c, that
expresses the fact that the total length is 75?
13
Line up
2c
d
75
Instead of d we can write 3c. 2c 3c 75 5c
75 c 15
14
Line up
2c
d
75
If c 15, what is d?
d 45
15
Line up
The length of the line is 32. What is an
algebraic expression of this fact involving x and
y?
3x 2y 32
16
Line up
Part of the line of length y is 1 unit longer
than the part of the line of length x. What is an
algebraic expression of this fact?
y x 1
17
Line up
What is an equation involving only x, that
expresses the fact that the total length is 32?
18
Line up
Instead of y we can write x 1. 3x 2(x 1)
32 3x 2x 2 32 5x 30
, so x 6
19
Line up
If x 6, what is y?
y 7
20
Line up
The length of the line is 3a. What is an
algebraic expression of this fact involving a and
b?
23 b 3a
21
Line up
Part of the line of length b is twice the length
of a. What is an algebraic expression of this
fact?
b 2a
22
Line up
What is an equation involving only a, that
expresses the fact that the total length is 3a?
23
Line up
Instead of b we can write 2a. 23 2a 3a So a
23
24
Line up
If a 23, what is b?
b 46
25
Line up
The length of the line is 5c. What is an
algebraic expression of this fact involving c and
d?
13 d 5c
26
Line up
Part of the line of length d is 3 units longer
than the part of the line of length c. What is an
algebraic expression of this fact?
d c 3
27
Line up
What is an equation involving only c, that
expresses the fact that the total length is 5c?
28
Line up
Instead of d we can write c 3. 13 c 3
5c 4c 16 So c 4
29
Line up
If c 4, what is d?
d 7
30
Line up
The length of the line is 8x. What is an
algebraic expression of this fact involving x and
y?
2y 38 8x
31
Line up
Part of the line of length y is twice as long as
x, plus one unit. What is an algebraic expression
of this fact?
y 2x 1
32
Line up
What is an equation involving only x, that
expresses the fact that the total length is 8x?
33
Line up
Instead of y we can write 2x 1. 2(2x 1) 38
8x 4x 2 38 8x 4x 40
, so x 10
34
Line up
If x 10, what is y?
y 21
35
Line up
Five times Robs age added to Toms age makes 53,
their mothers age. Toms age is 3 less than
twice Robs age. How old are Rob and Tom?
If x represents Robs age and y represents Toms
age, then 5x y 53 and y 2x 3. Leading to
x 8, y 13. Rob is 8 and Tom is 13.
36
Line up
Work out the values of the two variables when
both equations are true
v u 1 and 5u 2v 65
u 9 and v 10
If different equations involving the same
variables are assumed to be true at the same
time, the equations are referred to as
simultaneous equations.