Download Substitution/Elimination Test

Substitution/Elimination Test
Solving Systems by Substitution
1) Solve one equation for one variable
2) Substitute the expression from step 1 into the other equation, and solve for the other
variable
3) Substitute the value from step 2 into the original equation and solve
Examples:
1) y = x + 4
y = -1 + 4
y=3
4x + y = -1
4x + x + 4 = -1
5x + 4 = -1
5x = -5
x = -1
(-1,3)
2) x = y + 5
x = -2 + 5
x=3
2x + y = 4
2(y + 5) + y = 4
2y + 10 + y = 4
3y + 10 = 4
3y = -6
y = -2
(3,2)
Try These:
1) y = x + 1
2x + y = -2
2) x = 4y – 1
2x + 2y = 3
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Solving Systems of Equations by Substitution
Name:__________________
______________________________________________________________________
1) y = 6x – 11
-2x + y = -7
2) y = x – 1
2x + 3y = -1
_______________________________________________________________________
3) y = -3x + 5
5x + 4y = -3
4) y = -5x – 17
-3x – 3y = 3
_______________________________________________________________________
5) y = -2
4x – 3y = 18
6) y = 5x – 7
-3x – 2y = -12
_______________________________________________________________________
7) y = 4x + 6
-5x – y = 21
8) x = 2y + 11
-7x – 2y = -13
_______________________________________________________________________
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_______________________________________________________________________
9) y = 5x – 2
-3x + 6y = -12
10) y = 5x – 3
3x – 8y = 24
_______________________________________________________________________
11) x = -3y + 1
-3x – 3y = -15
12) y = 5x + 19
-3x – 8y = 20
_______________________________________________________________________
13) y = x + 3
-3x + 3y = 4
14) y = 5x + 13
-6x + 6y = 6
_______________________________________________________________________
15) y = -5x – 13
3x + 3y = -3
16) y = -2x + 20
6x – 5y = 12
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Substitution Word Problems
1) A will states that Katherine will get 4 times as much as Jack. The total amount they
will receive is 12,000. Solve to find the amounts of money Katherine and Jack will
receive.
2) Gary makes 4 times as much as Pam. Together they made 67,000 for the year. How
much does Gary make? Pam make?
3) One company charges a service charge of $20 and $15 per hour to service your air
conditioner. Another company charges a service charge of $10 and $20 per hour to
service your air conditioner. For how many hours will the cost of each company be the
same and how much will the charge be?
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Solving Systems by Substitution
Algebra I Practice Quiz
Name:__________________
Solve the following systems by substitution:
1) y = 3x – 10
-2x + y = -5
2) y = -3x – 1
6x + 3y = -6
3) x + 6y = 4
y = 15x – 25
x = -4y + 6
4) y = 5x + 5
5) A will states that Chad will get 7 times as much as Penny. The total amount they will
receive is 24,000. Solve to find the amounts of money Chad and Penny will receive.
6) One company charges a service charge of $25 and $10 per hour to service your air
conditioner. Another company charges a service charge of $40 and $5 per hour to service
your air conditioner. For how many hours will the cost of each company be the same and
how much will the charge be?
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Systems by Linear Combination (Elimination)
How to solve systems by elimination:
1) Find or make opposites of either the x or y variables
2) Combine all terms vertically
3) Solve for the variable
4) Substitute the answer into one equation, and solve for the other variable
Example:
1) x + 2y = 7
3x – 2y = -3
4x
=4
4x = 4
4
4
x=1
1 + 2y = 7
-1
-1
2y = 6
y=3
2) 4x + 4y = 12
-4x +4y = 4
8y = 16
y=2
4x +4(2) = 12
4x + 8 = 12
- 8 -8
4x = 4
4 4
3) 3x + 5y = 10
x – 5y = -10
4x =
0
x=0
3(0) + 5y = 10
5y = 10
y=2
(0, 2)
x=1
(1,3)
(1, 2)
Try These:
1) 5x + 4y = -7
6x – 4y = -26
2) -9x + 2y = -24
9x – 6y = 0
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Examples without opposites:
1) 2(4x – y = 6)
3x + 2y = 21
8x – 2y = 12
3x + 2y = 21
11x = 33
8(3) -2y =12
24 – 2y = 12
-24
-24
x= 3
(3,6)
-2y = -12
y=6
Word Problem Example
The dance team sold t-shirts and hats for a fund raiser. It cost $20 for t-shirts and $5 for
hats. They sold 42 items and made $690.
Write an equation for money made:
Write an equation for items sold:
20t + 5h =690
-20( t + h = 42)
20t + 5h = 690
-20t – 20h = -840
-15h = -150
H = 10
t + 10 = 42
- 10 -10
t = 32
How many of each item did they sell? 32 t-shirts and 10 hats
Try This:
1) The price for 3 adults and 2 children is $18. The price for 1 adult and 6 children is
$22. How much is an adult’s ticket? a child’s ticket?
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Types of answers of systems:
1) Ordered pair
Ex: x = 2 and y = 4, so (2, 4)
2) Identity: All variables cancel
Ex: 8 = 8,
so infinite solutions
3) Non-equal: All variable cancel
Ex: 7 ≠ 4,
so no solutions
Examples:
1) 7x – 2y = 3
-7x + 2y = 5
0=8
No solutions
3) y = 3x – 2
2) 8x – 4y = 20
-4x + 2y = -10
-6x + 2y = -4
8x – 4y = 20
-8x +4y = -20
0=0
Infinite Solutions
4) y = -8x + 10
y = -8x + 4
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Elimination Practice
1) -4x – 2y = -12
4x +8y = -24
2) 4x + 8y = 20
-4x + 2y = -30
3) x – y = 11
2x + y = 19
4) -6x + 5y = 1
6x + 4y = -10
5) -2x – 9y = -25
4x + 9y = 23
6) 8x + y = -16
3x – y = 5
7) -6x + 6y = 6
-6x + 3y = -12
8) 7x + 2y = 24
8x + 2y = 30
9) 5x + y = 9
10x – 7y = -18
10)-4x + 9y = 9
x – 3y = -6
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11) -3x +7y = -16
-9x + 5y = 16
12) -7x + y = -19
-2x + 3y = -19
13) 16x – 10y = 10
-8x – 6y = 6
14) 8x + 14y = 4
-6x – 7y = -10
15) -4x – 15y = -17
-x + 5y = -13
16) –x – 7y = 14
-4x – 14y = 28
17) -7x – 8y = 9
7x + 8y = -9
18) 5x + 4y = -30
-10x – 4y = 12
19) -4x – 2y = 5
-12x – 6y = 15
20) 3x – 2y = 2
5x – 5y = 10
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21) 5x + 4y = -14
3x + 6y = 6
22) 2x + 8y = 6
-5x – 20y = -15
23) 7x – 3y = 10
-7x + 3y = 12
24) 8x + 4y = 16
8x + 4y = 16
25) -7x – 8y = 9
-4x + 9y = -22
26) 5x + 4y = -30
3x – 9y = -18
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Elimination Practice Quiz
Algebra I
Name: ________________________
Date: ____________ Period: ______
Solve by elimination. SHOW ALL WORK
1) 4x + 3y = 16
2x – 3y = 8
2) p + 4q = 23
-p + q = 2
3) -2x + 2y = -2
2x + 3y = 12
4) 2x – y = 2
2x + 3y = 22
5) 3x – 4y = 8
-2x + y = 3
6) 9x – 3y = 20
3x + 6y = 2
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