Simultaneous_Equations.pptvhhhbhhhhhvbhhh

Simultaneous equations

1. Simultaneous
Equations

2. A few hints . . .
(1)Scale up each term in one, or both
equations to make the same number in
front of eitherthe xterms orthe y
terms.
(2)Subtractif the signs in front of these are
the same.
(3)Addif the signs in front of these are
different.

3. 5x+y=20
2x+y=11
… (1)
… (2)
Number
the
Equations
3x =9
Subtract
(to get rid
of a letter)
Divide
(to find x)
x =3
Substitute
in (2)
(to find y)
2 x3+y=11
6+y=11
y=5
1

4. 7x+y=43
3x+y=23
… (1)
… (2)
Number
the
Equations
4x =20
Subtract
(to get rid
of a letter)
Divide
(to find x)
x =5
Substitute
in (2)
(to find y)
3 x5+y=23
15+y=23
y=8
2

5. 8x+3y=57
6x+3y=51
… (1)
… (2)
Number
the
Equations
2x =6
Subtract
(to get rid
of a letter)
Divide
(to find x)
x =3
Substitute
in (2)
(to find y)
6 x3+3y=51
18+3y=51
y=11
3
3y=33

6. 3x+y=19
x-y=1
… (1)
… (2)
Number
the
Equations
4x =20
Add
(to get rid
of a letter)
Divide
(to find x)
x =5
Substitute
in (2)
(to find y)
1 x5-y=1
5 -y=1
y=4
4

7. 7x+2y=32
3x-2y=8
… (1)
… (2)
Number
the
Equations
10x =40
Add
(to get rid
of a letter)
Divide
(to find x)
x =4
Substitute
in (2)
(to find y)
3 x4-2y=8
12-2y=8
y=2
5
2y=4

8. 9x+4y=82
3x-4y=-10
… (1)
… (2)
Number
the
Equations
12x =72
Add
(to get rid
of a letter)
Divide
(to find x)
x =6
Substitute
in (2)
(to find y)
3 x6-4y=-10
18-4y=-10
y=7
6
4y=28

9. Simultaneous
Equations
-Scaling up -

10. A few hints -Reminder . . .
(1)Scale up each term in one, or both
equations to make the same number in
front of eitherthe xterms orthe y
terms.
(2)Subtractif the signs in front of these are
the same.
(3)Addif the signs in front of these are
different.

11. 2x+3y=13
4x-y=5
… (1)
… (2)
Number
the
Equations
14x =28
Add
(to get rid
of a letter)
Divide
(to find x)
x =2
Substitute
in (2)
(to find y)
4 x2-y=5
8 -y=5
y=3
7
2x+3y=13
12x-3y=15
… (1)
… 3 x(2)
Scale up
one of the
equations

12. 6x+5y=57
3x+y=24
… (1)
… (2)
Number
the
Equations
-9x =-63
Subtract
(to get rid
of a letter)
Divide
(to find x)
x =7
Substitute
in (2)
(to find y)
3 x7+y=24
21 +y=24
y=3
8
6x+5y=57
15x+5y=120
… (1)
… 5 x(2)
Scale up
one of the
equations

13. 12x-2y=8
5x+y=18
… (1)
… (2)
Number
the
Equations
22x =44
Add
(to get rid
of a letter)
Divide
(to find x)
x =2
Substitute
in (2)
(to find y)
5 x2+y=18
10 +y=18
y=8
9
12x-2y=8
10x+2y=36
… (1)
… 2 x(2)
Scale up
one of the
equations

14. 7x-3y=29
2x+5y=20
… (1)
… (2)
Number
the
Equations
41x =205
Add
(to get rid
of a letter)
Divide
(to find x)
x =5
Substitute
in (2)
(to find y)
2 x5+5y=20
10 +5y=20
y=2
10
5y=10
35x-15y=145
6x+15y=60
… 5 x(1)
… 3 x(2)
Scale up
both of the
equations

15. 6x-2y=48
5x-3y=36
… (1)
… (2)
Number
the
Equations
8x =72
Subtract
(to get rid
of a letter)
Divide
(to find x)
x =9
Substitute
in (2)
(to find y)
5 x9-3y=36
45 -3y=36
y=3
11
3y=9
18x-6y=144
10x-6y=72
… 3 x(1)
… 2 x(2)
Scale up
both of the
equations

16. 2x+3y=75
7x+4y=191
… (1)
… (2)
Number
the
Equations
-13x =-273
Subtract
(to get rid
of a letter)
Divide
(to find x)
x =21
Substitute
in (2)
(to find y)
7 x21+4y=191
147+4y=191
y=11
12
4y=44
8x+12y=300
21x+12y=573
… 4 x(1)
… 3 x(2)
Scale up
both of the
equations