worksheet 4.1 simultaneous equations i name: · 2020-03-18 · 8 solve the following pair of...
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© John Wiley & Sons Australia, Ltd Page 1
WorkSHEET 4.1 Simultaneous equations I Name: ___________________________ 1 Solve the following pair of simultaneous
equations using the substitution method.
4 2
5 2 32x yx y= -- =
( )( )
( ) ( )( )
4 2 1
5 2 32 2
Substitute 1 into 2
5 4 2 2 3220 10 2 32
12 121
Substitute 1 into (1)4 2 1
4 26
x y
x y
y yy y
yyyxxx
= -
- =
- - =
- - =- =
= -= -= - ´-= +=
Solution: (6, -1)
2 Solve the following pair of simultaneous equations using the substitution method
3 7
2 5 48y xx y= -- =
( )( )
( ) ( )( )
( )
3 7 1
2 5 48 2
Substitute 1 into 2
2 5 3 7 482 15 35 48
13 131
Substitute 1 into 13 1 7
10
y x
x y
x xx x
xxyyy
= -
- =
- - =
- + =- =
= -
= -
= ´- -= -
Solution: (-1, -10)
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5 Solve the following pair of simultaneous equations using the substitution method.
2 22
3 4 53y xx y= -- =
( )( )
( )( )
( )
2 22 1
3 4 53 2
Substitute (1) into 2
3 4 2 22 533 8 88 53
5 357
Substitute 7 into 12 7 2214 22
8
y x
x y
x xx x
xxxyyy
= -
- =
- - =
- + =- = -
=
=
= ´ -= -= -
Solution: (7, -8)
6 Solve the following pair of simultaneous equations using the substitution method.
( )1 1 34
6 2 5
x y
x y
= - -
- =
( ) ( )
( )( )
( )
( )
( )
( )
( )
1 1 3 14
6 2 5 2
Substitute (1) into 216 1 3 2 546 1 3 8 20
6 18 8 2026 26
1Substitute 1 into 1
1 1 3 141 1 341 2412
1Solution: , 12
x y
x y
y y
y yy y
yyy
x
x
x
x
= - -
- =
´ - - - =
- - - =
- - - =- =
= -
= -
= - - ´-
= - +
= ´
=
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7 Solve the following pair of simultaneous equations using the elimination method.
122124
=+=-yxyx
( )( )
( ) ( )
( )
4 12 1
2 12 2
1 2 : 6 244
Substitute 4 into 22 4 12
8 124
x y
x y
xxxyyy
- =
+ =
+ =
=
=
´ + =+ =
=
Solution: (4, 4)
8 Solve the following pair of simultaneous equations using the elimination method.
142454=+--=+yx
yx
( )( )
( ) ( )
( )
4 5 1
4 2 14 2
1 2 : 3 93
Substitute 3 into 14 3 5
4 82
x y
x y
yyy
xxx
+ = -
- + =
+ =
=
=
+ = -= -= -
Solution: (-2, 3)
9 Solve the following pair of simultaneous equations using the elimination method.
132425-=+
=-yxyx
( )
5 2 243 1
(2) 2: 6 2 2(1) (3): 11 22
2Substitute 2 into 2
3 2 16 1
7
x yx yx y
xxxyyy
- =+ = -
´ + = -+ =
=
=
´ + = -+ = -
= -
)3()2()1(
Solution: (2, –7)
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10 Solve the following pair of simultaneous equations using the elimination method.
31214098
=+=+yxyx
( )( )( )( )
( )
8 9 0 1
14 12 3 2
(1) 4: 32 36 0 3
(2) 3: 42 36 9 4(4) (3): 10 9
9109Substitute into 1
1098 9 0
1072 9 010
369545
x y
x y
x y
x yx
x
x
y
y
y
y
+ =
+ =
´ + =
´ + =
- =
=
=
´ + =
+ =
= -
= -
Solution: ÷øö
çèæ -
54,
109