Download Study Guide and Intervention

DATE
NAME
7-4
PERIOD
Study Guide and Intervention
-
Elimination Using Multiplication
Elimination Using Multiplication
Some systems of equations cannot be solved
In such cases, one or both equations must
the
equations.
by
adding
or
subtracting
simply
first be multiplied by a number before the system can be solved by elimination.
ru
ffi
r*105r=3
4fi + 5Y:5
2r
use elimination to solve
the system of equations.
use elimination to solve
the system of equations.
If you multiply the second equation by
you can eliminate the y terms.
(+)
3x-2y--7
- 5Y: lg
If you multiply the first equation by 2 and
the second equation by -3, you can
eliminate the r terms.
-2,
x*I}Y:
3
:
10y
-10
-8r
: -7
-7x
-7x -7
-7 -7
-:-)c:l
6x- 4Y:-14
: -30
71Y : -44
11v -44
11 11
!:-4
(+) -6.r + 15y
I for x in either equation.
1+10y:3
1+10y-1-3-1
IOY=2
l}y=2
10 10
1
\) ::
Substitute
The solutio"
Substitute
-4 for y in either
equation.
3x-2(-4):-7
3r*8--7
3r+8-8:-7-8
3r : -15
3x -15
33
-:x: -5
i. (r, f).
The solution is
(-5, -4).
reFlffirlc
Use elimination to solve each system of equations.
L,2x+3y:6._il ,r\
x1-2Y=$ '-''"i!
4.4x+5Y:6 , t r\
6x - 7y : -20 '.-i' {'r
7"4s-t9 .r -i\
" 5s * 2t:8 t'j -:
i
10.6r-4y: -8,-i,d'i
i':l
4x+2Y:-3'
*.3: : 4- i _i. I )
-trL*2n:5 \
2r.2rn
5.1, - 39 :-?2 ' ;+.
.])
t:
2c-d=I0
8.4a-3b:-8r-.L
i
2a + 2b:3
rl
,!
l1-.4x*2y:-5r i- .j-\
-%c - 4Y : L '-t]' 'l '
- b :2 "i''iti\
a+2b:3
6.3x-4y:-4.*,;
-jir'/
x*3Y = -10
9.2x + 2y:5 I il ir)
4x-4Y:L0'J't -''
3.3a
Lzt2x +y:3.5
'"
-x -l 2Y : 2.5
13: GARDENING The tength of Sally's garden is 4 meters greater than 3 times the width.
''"
The perimeter of her garden is 7i meters. What are thetimensions of Sally's garden?
'1
14.
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Anita is
f
,1
{f;
years older than Basilio. Three times Anita's age added to six times Basilio's
ase is 86. How old are
s Glencoe/McGraw-Hill
Anita and Basilio? Hnl
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Glencoe Algebra
1
PERIOD
Study Guide and Intervention
pontinued)
Elimi nation Using M ultiplication
Determine the Best Method The methods to use for solving systems of linear
equations are summarized in the table below.
The Best Time to Use
Method
Graphing
to estimate the solution, since graphing usually does not give an exact solution
Substitution
if one of the variables in either equation has a coefficient of 1 or
Elimination Using Addition
if one of the variables has opposite coefficients in the two equations
Elimination Using Subtraction
if one of the variables has the same coefficient in the two equations
Elimination Using Multiplication
if none of the coefficients are 1 or -1 and neither of the variables can be
eliminated by simply adding or subtracting the equations
-1
reDeterminethebestmethodtosolvethesystemofequations.Then
solve the system.
&r+2Y=20
-?.s+4Y=-16
Since the coefficients of r will be additive inverses of each other if you
equation by 3, use elimination.
6x + 2(-2) : 20
20
6x
multiply the
* 2Y:
(+) -Gx + L2y : -48
: -23
L4y
-28
L4 - 14
L4Y
y:-2
substitute
second
-2lor yin
either equation.
Multiply the second equation by 3.
Add the tvvo equations. x is eliminated.
6x
Divide each side by 14.
6x - 4:20
- 4 + 4 = 20 + 4
6x:24
6x _24
Simplify.
66
x:4
simptify.
Add4toeachside,
Simplify.
Divide each side by 6.
Simplify.
The solution is (4, -2).
Determine the best rrqgthgl to solve each system of equations. Then solve the system.
l.x-2y:3
t i r\
\--lt7J
X-!:1
2.m*6n:-8
m:2nt8
4.4x+y:I5
t1.j)
-x-3Y:-I2"-
5.3c
7.4x:
8.x: -2y
2y
-
70:
X-l 2Y=$
i)
\ -iii'''l
- 4b:
2a*4b: -]o i-.. 5)
LO.4a
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r,,
a\
'..-f,-'t,)
1-'t:
t"i''
: -G t-1
-2x-10Y=2\'i'
LL.4x + 10Y
422
{i.l
\"-' -i\tl
* 2y: -e
[-i, -'i]
y=M
..
- d: L4 iL,'l)
"'i"--f,:
r'*
4x + 4y -- -10
3.a-b:6
a=2b*7
6.x
r
.J
"i\
^t,/
tl
9.2s-3t:42 i \ .r'\
Bs * 2t : 24 i.Ii'*tt,l
u'
?*:*'r-:to t' i, -*'i )
Glencoe Algebra
1
PERIOD
DATE
Skills Practice
Elimination Using Multiplication
Use elimination to solve each system of equations.
* 2Y: -g
x-Y = -13
L.x *
!: -9
- 2Y :12
i.j, -ll/
3.?.rc + 5y:3
-x*3y--7
2.3x
5x
lt'
i4,\
| * ft J I,
,
L,J
\
;.t
Brl
4.?e, +
{1,,i
O
-n
" ,V,nr
7.5x+3y:-10
8.2x +
3x+5y--6
3Y:
14
3x-4Y:4
!;''1 -l\
:lf
i*]
\ .r. lt\
v.r
9.2* - 3Y:2L
i
t
ir\
r
i -.,
-
l\
6.2'x + Y
;-t ;i
5x
..
:
5x*3Y:)
6.4tc-2Y:-L4
3r-Y:-g
2Y
3
-4x-4Y:-8
,\
I
\
y=
L
10.3r*2Y:-26
4x-Ey--4
:25
i r
t. "5)
.
\-'
,,\
}|A:
il
: -3
3x*3y:9
11.3r-6y:-3
?.tc + 4Y :30
12,5x
;?
i)
..1 +/
'f
2Y
i-.11.)
--_'-,w)
,13. TWo times a number plus three times another number equals 13. The sum of the two
*
numbers is 7. What are the numbers?
"-+
..14.
*'
.inil
-
|
Four times a number minus twice another number is
is -1. Find the numbers.
-
16. The sum of the two numbers
-:t ittr,.i ,i
o,i-lr.Si
Deterrnine the best mg!Ig_4 to solve each system of equations. Then solve the system.
;..15J%
* 3y:19
5x+2y--8
wv:2*
3x + 2Y :35
itg; gr - 4y
"'' 4x + 5y
: L7
:2
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41
r
f*rl
116,8r-7y=78
{i+
''3r+7Y:26
''til t)
/ l- l/'r)
ty:6
!8i3r
" 3x*!:3
-;)
t?Oiy: 3r *
('t1,
'3x-y:-l
423
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rnfrfi itQirJ
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Glencoe Algebra
1
DATE
NAME
PERIOD
-
Practice
Elimi nation Using Multiplication
Use elimination to solve each system of equations.
Y: -I
3x-2Y:1
2.5x
t.2x -
- 2Y:
3.7x -t 4Y : -4
lrc + 8y :28
-10
3x-f 6Y:$6
;
i,-1" -5)
4.2x-4Y:-22
3rtBY:$g
5x-3Y:L6
n\
1
l,*j)
- lp: -,
x+fl:0
* O.5y : -2
id:o rr
\
-3x-5Y:-IL
ul, -il
{.2';2"*4y:27
*
v
t.-r"i,
5.3r*2Y:-g
5x-BY:4
{,-'},7)
:,
tl
6.4x-2Y:32
i-:], lL))
qojzr
1
\+ ",6)
i,br3)
j,4l
,_ 4
i
"
'.\
times a number plus frve times another number is -13. The sum of the two
ifOlnignt
\-" numbers is 1. What are the number^t *
*
sI
i, ullli T
another number equals 4. Three times the first
number plus four times the other number is 7. Find,the numbers.
t*o times a number plus three times
iff:
uJ
1j' ..r'; *1
Determine the u"#r#Strrod to solve
system.
'f 7Y : 3
2x-7Y: -38
L2.5x
i!E]*
:
2y +
"""n
"i"tff'1,
.n1r",rons. Then solve the
t-y,,1) i};T;:A=r_r, y;,,6)
tn.
-u.*;fl:_t, i-1, -{)
6 lntrni'i-Vlil [9i- & -t 3y :: -2 t:u'i}lLlfll,Rl{ir'-: lr*
4x + 3Y 3
(.t-,,3J
'*.
i' -, : t
ifrl
tJ
f lfrfnfrf CE Gunther invested $10,000 in two mutual funds. One of the funds rose 67o in
orru year, and the other rose 97o in one year. If Gunther's investment rose a total of $684
in one year, how much did he invest in each mutual fund?
1
='x - 2Y :9
5
ffll{ly n't'r"r'n;
$?
iuu
rn thu ul, tlinli ul'{.l
S
)silli ,il tnt 4 t: 'hr"rn'"i
ifb. C4TOEING Laura and Brent paddled a canoe 6 miles upstream in four hours. The
"'-' return trip took three hours. Find the rate at which Laura and Brent paddled the canoe
in stiil water.
1.75 {npn
€0, trtUMgER THEORY The sum of the digits of a two-digit number is 11.If the digits are
'- 1."u"rr"d, the new number is 45 more than the original number. Find the number.
o Glencoe/McGraw-Hill
Glencoe Algebra
1