SELF CHECK! Make sure you are prepared for this test!STUDY!
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Transcript of SELF CHECK! Make sure you are prepared for this test!STUDY!
SELF CHECK!
Make sure you are prepared for this test!
STUDY!STUDY!
m = —11
m = —-2 3 ( 3, 4 )y = mx + by = mx + b
m = —54
m = —-11 ( 4, 1 )
y = mx + by = mx + b
one solution no solution infinite solutions
ANY 2 lines that cross (intersect)
at one point.
ANY 2 lines that are parallel
(never intersect).
ANY 2 lines that are the exact
same line!
If one equation in a system was y = x + 3,
the “solution to a system” must be
a point on that line!
(must make the equation TRUE)
Complete the ordered pairs:
( 5, ___ )
( 2, ___ )
( 1, ___ )
( –3, ___ )
( 4, ___ )
( 3, ___ )
( 0, ___ )
( –5, ___ )
y = 5 + 3
8
5
4
0
7
6
3
–2
“is” is theEQUAL SIGN!
==
b + g = 29
10 less than meanssubtract 10.– 10
“twice the # of girls…
2g
Total of 29 students…Add boys & girls.
“The # of boys is…”
b = ( )
( 2g – 10 ) + g = 293g – 10 = 29
+ 10 + 103g = 39g = 13
13 girls
Use the 1st equation:
b = 2g – 10 b = 2(13) – 10 26 – 10
b = 1616 boys
( )
–2 ( 7 – 2y ) + 3y = 14 Dist. Prop.
– 14 + 4y + 3y = 14C.L.T.
– 14 + 7y = 14+ 14 + 14
7y = 28y = 4
Use the 2nd equation:
x = 7 – 2y
x = 7 – 2(4)
7 – 8
x = – 1
( , )–1 4
Since one equation has a variable by itself… SUBSTITUTION.Since one equation has a variable by itself… SUBSTITUTION.
( ) (( ) (– 1)– 1)
3x + 8y = 14 –3x + 4y = – 2
12y = 12y = 1
Use either equation:
3x – 4y = 23x – 4(1) = 2
3x – 4 = 2 + 4 + 4
3x = 6 x = 2
( , )2 1Both standard form… use elimination!Both standard form… use elimination!
19 people…add adults and students
a + s = 19
“5 hours” is EXTRA INFO!
adults cost $9 9a
students cost $4
4s everyone cost $111
+ = 111(( )) (-4)
– 4a – 4s = – 76 9a + 4s = 111
5a = 35a = 7
7 adults
The 1st equation looks easier:
a + s = 197 + s = 19–7 – 7
s = 12
12 students
Both standard form… Both standard form… use elimination!use elimination!
3/2 (-6) – 9 = – 18
3/2 (-3) – 9 = – 13.5
3/2 (0) – 9 = – 93/2 (3) – 9 = – 4.53/2 (6) – 9 = 0
– 4/3 (-6) + 8 =16
– 4/3 (-3) + 8 =12
– 4/3 (0) + 8 =8
– 4/3 (3) + 8 =4
– 4/3 (6) + 8 =0
Which ordered pair is the SAME in both tables?
( 6 , 0)
( 6 , 0 )
( )( )
4x – ( 2x – 5 ) = 7 Dist. Property
4x – 2x + 5 = 7C.L.T.
2x + 5 = 7 – 5 – 5 2x = 2
x = 1
Use the 1st equation:y = 2x – 5
y = 2(1) – 5 2 – 5
y = – 3
( , )1 –3Since one equation has a variable by itself… SUBSTITUTION.Since one equation has a variable by itself… SUBSTITUTION.
– 6x = – 54
x = 9 Use either equation:
– 2x + 8y = – 26
– 2(9) + 8y = – 26
– 18 + 8y = – 26
+ 18 + 18
8y = – 8
y = – 1
( , )9 – 1Both standard form… use elimination!Both standard form… use elimination!
( )( )
1 + x = 2x + 6 – 2x – 2x 1 – x = 6 – 1 – 1 – x = 5
x = – 5
Choose either equation:y = 1 + x
y = 1 + (–5)
y = – 4
( , )– 5 – 4
– 4
Since one equation has a variable by itself… SUBSTITUTION.Since one equation has a variable by itself… SUBSTITUTION.
add nickels & dimes n + d
103 coins
= 103nickels are
worth 0.05 ea.
0.05n dimes are worth 0.10 ea.
0.10d
All the coins are worth $8.00
+ = 8.00
The problem says to write the system…
NOT SOLVE IT!
Let c be packs of cards…and let t be tattoos.
Jose 4c + 3t Jose spent $11.45= 11.45
L.C. 1c + 4t L.C. spent $9.85= 9.85(( )) (– 4)
4c + 3t = 11.45– 4c – 16t = –39.40
– 13t = –27.95 t = 2.15$2.15 per tattoo
Use one of the equations:
c + 4t = 9.85c + 4(2.15) = 9.85c + 8.60 = 9.85
– 8.60 – 8.60 c = 1.25
$1.25 per pack of cards
Both standard form… Both standard form… use elimination!use elimination!
(( )) (–2)
2a + 2b = 16–2a – 2b = 16
0 = 32True? NO!
No Solution
No SolutionNo Solution
Both standard form… use elimination!Both standard form… use elimination!
How many less?(subtract)30 – 10
20
Animals total?(add)
30 + 10
40
How many times?(divide)30 ÷ 10
3
( , )4 3
Failure to prepare means you must be prepared to fail.
STUDY!STUDY!