Simultaneous equations :
30C -
y
=
10
9×2
'
20
y
- =
I
8g 9oc= -
-
Roc -
10x =/ Rewrite then sub
① ①
8g 9x= I 3K IO
y
-
- - -
-
I 922 ( 3K IO ) 2=20
10g t 120C =
- -
-
② 32 -
360C = -
4 X4
-
soy + 360C =3 113 ② Expand :
9×2 - (9×2-60×+100)=20
③ I landed the x 's then added the
2g
=
-
out sums
-
I 4)
y= change sign the =O
9×2 -
9×2+60×-100 -
20=0
Get x : Sub in the values
① C I) I g) Solve
8g ax
-
- = -
:
-
doc =3 box = 120
x = 2=2
6) Work for :
g
Simultaneous equations with squares
:
y
-
-
sczo ) -
lo
SO
y
=
atb = 7 I
AZ + b 2=16 2
① Substitution :
a = 7 -
b
b 2=25
2
( y -
b) +
② Expand :
Z
( 7 b) -
+ b. 2=25
49 -
Kib tbztbz = 25
③ add like terms :
Z
2b -
14 b -124=0
BZ -
Tb +12=0
④ Facto rise :
( b 3) ( b 4) =D
- -
⑤ get variables :
b -
- 3
; b =L, C 4 's 3)
a- 4 ; a =3 ( 3 ; 4)
, SOLVING LINEAR INEQUALITIES :
2x +375
2x > 2
X > I
< ? 9
I
-2 (x + 3) 78
)
(x -13) -
Li ( when x or ÷
by -
swap sign
X
-
7
• ••
< .
p
>
-
7
-
9 2x -
3 3
-
b 2x b
-
3 x 3
•• O
< >
is g
-
2 ,
-
boo 10 E -
coefficient ]
-
b -
boo 6
- b
(t ) ( x) C -
t )
13 x > - I
Koc
= I
simply re order into
reading from left to
right
-
way
-
-
, Ord Sum :
Word problems number
involving relationship :
a) A ¥ exceeds It
another
by 10 .
the two numbers
are in ratio s :3 find the two numbers .
y=oc
-110
ociy
x x
-
-
=-3
3 :S -110
y
= x
LCD :
(x -110)
① I = 3- Cx -110)
x -110
5
2 52 =3 Cx -110 )
3 2x = 30
↳ a = IS
b) A # consists of two
digits - The sum is 11 .
It the
digits are
# number Find the
reversed ,
the new is 45 more than the
original .
two
digit number .
, at Il
y
-
-
11 : 10K ( ) 9×-111
y
=
-
OC -
t Il -
x =
bigger )
(
10g + x
smaller #
Bigger # 45 lock a) too
-
-
= 110 -
90C
( 110 - 9K ) - 9×-1111=45
110 -
90C -
90C -
11=45
49 -
180C =L, s
-
180C = ↳S - 99
- 180C =
-
54
X =3
30C -
y
=
10
9×2
'
20
y
- =
I
8g 9oc= -
-
Roc -
10x =/ Rewrite then sub
① ①
8g 9x= I 3K IO
y
-
- - -
-
I 922 ( 3K IO ) 2=20
10g t 120C =
- -
-
② 32 -
360C = -
4 X4
-
soy + 360C =3 113 ② Expand :
9×2 - (9×2-60×+100)=20
③ I landed the x 's then added the
2g
=
-
out sums
-
I 4)
y= change sign the =O
9×2 -
9×2+60×-100 -
20=0
Get x : Sub in the values
① C I) I g) Solve
8g ax
-
- = -
:
-
doc =3 box = 120
x = 2=2
6) Work for :
g
Simultaneous equations with squares
:
y
-
-
sczo ) -
lo
SO
y
=
atb = 7 I
AZ + b 2=16 2
① Substitution :
a = 7 -
b
b 2=25
2
( y -
b) +
② Expand :
Z
( 7 b) -
+ b. 2=25
49 -
Kib tbztbz = 25
③ add like terms :
Z
2b -
14 b -124=0
BZ -
Tb +12=0
④ Facto rise :
( b 3) ( b 4) =D
- -
⑤ get variables :
b -
- 3
; b =L, C 4 's 3)
a- 4 ; a =3 ( 3 ; 4)
, SOLVING LINEAR INEQUALITIES :
2x +375
2x > 2
X > I
< ? 9
I
-2 (x + 3) 78
)
(x -13) -
Li ( when x or ÷
by -
swap sign
X
-
7
• ••
< .
p
>
-
7
-
9 2x -
3 3
-
b 2x b
-
3 x 3
•• O
< >
is g
-
2 ,
-
boo 10 E -
coefficient ]
-
b -
boo 6
- b
(t ) ( x) C -
t )
13 x > - I
Koc
= I
simply re order into
reading from left to
right
-
way
-
-
, Ord Sum :
Word problems number
involving relationship :
a) A ¥ exceeds It
another
by 10 .
the two numbers
are in ratio s :3 find the two numbers .
y=oc
-110
ociy
x x
-
-
=-3
3 :S -110
y
= x
LCD :
(x -110)
① I = 3- Cx -110)
x -110
5
2 52 =3 Cx -110 )
3 2x = 30
↳ a = IS
b) A # consists of two
digits - The sum is 11 .
It the
digits are
# number Find the
reversed ,
the new is 45 more than the
original .
two
digit number .
, at Il
y
-
-
11 : 10K ( ) 9×-111
y
=
-
OC -
t Il -
x =
bigger )
(
10g + x
smaller #
Bigger # 45 lock a) too
-
-
= 110 -
90C
( 110 - 9K ) - 9×-1111=45
110 -
90C -
90C -
11=45
49 -
180C =L, s
-
180C = ↳S - 99
- 180C =
-
54
X =3
