•
Review for h{\cd . For #1 - 2, SHOW whether or not the iven oint is a solution to the X-2 Y =-2
\4, 3);
1
1
{ y=-x+
2
• I
2
2) (3,-1);
Y=-"3 x +1
{
4x- Y = 11
Solve#3 - 5 b
y=2x­
{y=-x+9
3)
5)
Answer _ _ _ __
Answea- _ _ _ __
•
Answer _ _ _ __
mnotebook paper, use substitution to solve #6 - 9.
x=y+4
lx=40-5y
7)
x=y+S
{ 2x-5y=1
9)
I
(
8)
Y=3X+2
{ 2x- y = 1
' -3x+y=9
{ 4x+2y=S
, {X+2Y =14
2x=3y
On not eb00k: paper, use e1iminabon
. to so1ve #10 ­ 13
10)
6x-7y= 28
e
'VA.;- :Jy
12)
11)
.JA.Y
, J. '"
7Y,=41
,
6x+5y=-7
X
3x+4y=4
{ r+y=4
7) Solye by substitution:
.
,­
•
l
'J.:J
Y
13) {2x+3 =2
-
5) Solve by graphing:
4x+5y=22
3r-y=-S'
f 1Y
{lr-3
X+
=7
y=3x+8
,6) Solve by any. method:
8) Solve by elimination:
{2r+2Y=2
e
y=l-r
r + 4Y =5.
'
r+y=2
10) Write a system of equations to describe this
problem: A S()"foot long piece of rope is cut into two
.
__
-pieses; ..TJle eiffereRGe-iA-theij;leRg!As-is 8,feet: -" -'
.
.'
Find the lengths of the two pieces.
.
11) Phil' has 50 coins, aU either nickels or dimes. The total value of the coins is $4.15. Write and solve a
system of equations to find the number of dimes he has.
Y =17'
~~~:: ~~~i~~~: ?!=1Y..~-12~~~ __ ~..._,_'
-
For #26 - 29, defme two variables, write and solve a s stem of uations, and answer the lestion.
26) Warren has 100 coins, all either dimes or quarters. The 27) Five pens and three notebooks cost $15.75. Two pens
total value of the coins is $21.40. How many of each type
and four notebooks cost $14. How much does each pen and
of coin does he have?
each notebook cost?
•
I
29) A manufacturer has an order for 500 gallons of a 35%
acid solution. The plant manager has on hand Solution A,
which is 25% acid and Solution B, which is 50% acid. How
many gallons of each type should be mixed to fill the order?
28) A health food store wishes to blend peanuts that cost
$1.20 Ilb with raisins that cost $2.1 Ollb to make 50 lbs of a
mixture that costs $1.471lb. Howmany pounds of each are
needed?
~
Be sure to ex
1) {y
our answers as inte ers or fractions, NOT decimal,s.
=2x-S
2)
y=7-x
llX-2Y =-1
3)
{ Sx+7y=8
Solve
4) {y =-2x-4
y=9x+S
ttl- 9 using the best method (elimination or substitution) WITHOUT using a calculator. You
5)
8)
y =4x-7
{ x=2y-14
2x+Sy=20
2
y=--x+4
S
7x+2y=S
{ 4x+3y=-12
of
6)
use a calculator to
y=10-2x
3x- y = 30
2
9)
X?3((Y+l))
S S
x='3 '2- y
work. 7)
4x+3y=1
7x+4y =-7
10) Solve by graphing on graph
paper: { y=2-x
x-3y=-18
,)
•
--.->0'-
,,~..
aM! p
4
N_W;::;
-~
%.
e
,~
Review for },f\CL \ ­
For #1 2, SHOW whether or not the given point is a solution to the given system
x-ZY=-Z
Z
1
---x+
~4, 3); { y = ~ x + 1
2) (3. -1); {
:~_
~~
'!
VO
;=11
Solve #3 - 5 by
3) { y=2x.
y=-x+9
5) {Y=3X+2
2x- Y= 1
~cd)l
-I
y=-2x+4
.)
nnotebook. ¥ .....y .......... ,
w.,;r_
x=y+4
, x=40-Sy
8)
{Y=~X-4
4)
h " "
g .... v~ ...............v.u.
'"""
U'\J
lve#6 -9 7) {-3X+Y=9
C'O,(.e)
{ x=y+5
2x-5y=1
(-ll(P)
4x+2y=8
. {X+2 Y =14
2x=3y
(fd)~)
(~J4 )
9)
On notebook paper, use elimination to solve #10 - 13.
6x-7y::::28
10)
( 1\ O.,l;T.JY,
.L"-
12) .{2X-7Y' =41
,
6x+Sy=-7
,--)
(.(1
11)
./
J.A.
13)
('3\-5)
..
5) Solve by graphing:
4x+5y=22
'L
{ x+y=4 . (:/ ~
.
~
3x-y=-S
(-I 5")
­
e
L
-
{2X+3 Y =2
3x+4y=4
Y
7) Solve by substitution: ex+2 =7 ' )
,~
y=3x+S
: .•. ." {2X - 3Y =17
,-
(~i
;.L.J
J
J
./
~
'(l/j-J.) "
. ,
.',
.6) Solve by ~11Y method:
'
{
.
2x+2 =
Y .~, .
Y = 1- x
Y'f'I'..f) 111"1
.
eX+4Y=5~
8) Solve by elimination:'
9,.1 ~
.
'
x+y=2
(C/ /)
10) Write a system of equations to descrtbe this
,
),' ,
problem: A 50-foot long piece of rope is cut into two
• -:;:~.':--- 5x3 =__
29 . . . . . . . -~_....-::-.-.
'.
.
"
. a·feet:-'__
-----:""-~-'
~._.~Y...
,pleses;-lhe Eiifferer:lse-iR-then;leAgtRs-1S
.......
'. '
'
.:'
Find the lengths of the two pieces,
11) Phil' ha~ 50 coins, at! either nickels or dimes. The total value of the coins is $4.15. Write and solve a
'
.
system of equations to find the number of dimes he~has.
9) Solve bY"ellmrnation:
,
/c;,)/Y.+ 'a:S-O @
tx- 11 =5
';.::dj )aX:;~
.
-
Xl~~5t>
.-IX f.~~~ ~/S-
., (S2:> -'1) f. ~H :. :t.1SS -. I ~ f. {)'O~ VZ/. 't<;
$
y.::./7
*,G ~'3
.' ..,;.
'.'~
-
~ cJ ... : 100
f> . .
.1
,@OpdA'='Is-':7SdP.j.'ff)
'P e" J. S""o
f- .;).~~ -::. ~,. 40
d
d
=IL{
·XI=1,. .~= j') (~lX.
A= 300
8= aDO
r. rs-
.
A+8:~oo_
J.,\
'P;;-3)"
n:."~ ...,~
,..ll/ .
@'P+-t":50
I.ap .,.::;.1,.. =:l~7(S6)
:: 1fDFor #26 - 29, de e two variables, write and solve a system of equations, and answer the auestion.
26) Warren has 100 coins, all either dimes or quarters. The 27) Five pens and three notebooks cost $15.75. Two pens
total value of the coins is $21.40. How many of each type
and four notebooks cost $14. How much does each pen and
of coin does he have?
each notebook cost?
to
•
I
29) A manufacturer has an order for 500 gallons of a 35%
acid solution. The plant manager has on hand Solution A,
which is 25% acid and Solution B, which is 50% acid. How.
many gallons of each type should be mixed to fill the order?
28) A health food store wishes blend peanuts that cost
$1.20 Ilb with raisins that cost $2."10Ilb to make 50 Ibs of a
mixture that costs $1.47/1b. How many pounds of each are
needed?
3)
Solve #1-9 using the best method (elimination or substitution) WITHOUT using a calculator.
. You may. of course. use a calculator to check vourwork.
5) ~ y=4x-7
6). {Y:::lI0-2X
x=2y-14
3x-y=30
x ~ i (y + 1)
2X+SY= 20
8)
2
9)
{ y=--x+4
5
­
tt)
I?J'Y :: 3
.3
... -/~
(~) -to)
_ 3(1)(+'11' "'-1)
It/; ~ f 1J...'i .:: '(
I-
JJ.'i
-~ ~
w:
~
c:tJ
­
~~-.s -s-(~J1)
~;;~
.
#
.II:'
1'1>7
(
~qx"3~ :: i)
~ J.1'f
77)<-/<1
'1~
~
_
-7
4
"/4
I~
;:: q
-
3Y~Of~x~5D
.~.= -~(p
5x ~ i/o
1:
IJIl
Ct
-.
u
f
,X-ro
-~)
Sf! -3)
cJ(d 1-/)':=
l
fin.
x':: 8
:/0 ..... I(p
If'd
=-U
CS)-lt)
ta"
CD 1(3
(1J }'I.OO1e-1
~~B~-~~
(:J) t}) ~1I
- '.;>. 'i tOl )3f/".~)
.
.
(3) ~ -; tf~4-('-I) (0 3x- (10 -~)l) =?J:.
-=.:('8) -/'1
~=~
~ 7~ :: ~
tlYVi,S
flo SoluJ;
Y =2-x
x-3y=-18
X'= Yf>7
.2 'f
'o0~ -~
-5111:'
{
.
(o'x
5 7x
0 •1J.
paper:
:1(5).. ... 7~a ~ f> )
;)./)< ,(, ~ • IS"­
.::...{l() 't' I-_lQ
.=!
qt'3)~3~
({). J. 3
3
5 5
CDtllx -J l1 .. -I
cJ(L/>c f 3 a - -I:J..)
l( •
10) Solve by graphing on graph
x='3(2- Y )
GJ3C!k f ~~.:: ~
To
j
.....
. 7) {. 4x+3y=1
.
7x+4y=-7
J~ I--;h;; ~-"S"Lt
I}~.~
d
~,,'1.'" :~ (~,1.)~
~.-z.
13
Y"x I'(p
(10
(-3J~)
i
~
.
•