Download Math Connections Systems of Equations Practice B

Name
LESSON
Date
Class
Practice B
11-6 Systems of Equations
Solve each system of equations.
1. y 2x 4
y x1
2. y x 10
yx2
3. y 2x 1
y 3x 6
4. y 2x
y 12 x
5. y 2x 3
y 2x 1
6. y 3x 1
yx1
7. x y 0
5x 2y 3
8. 2x 3y 0
2x y 8
9. 2x 3y 6
4x 6y 12
10. 6x y 14
2x 3y 6
11. The sum of two numbers is 24. The second number is 6 less
than the first. Write a system of equations and solve it
find the number.
15. Kerry and Luke biked a total of 18 miles in one weekend.
Kerry biked 4 miles more than Luke. Write a system of equations
and solve it to find how far each boy biked.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
47
Holt Mathematics
Practice C
LESSON
11-6 Systems of Equations
Practice B
LESSON
11-6 Systems of Equations
Solve each system of equations.
Solve each system of equations.
1. y 3x 1
y 2x
2. y x 10
yx2
1. y 2x 4
y x1
(3,2)
2. 2x 3y 12
x 4y 5
15, 25
(4,6)
4. y 2x
y 12 x
3. y 2x 1
y 3x 6
( 1, 3)
(4,8)
no solution
There are an infinite number of solutions.
1
8. y 4x 1
7. 2y 5x 5
7y 3x 32
x 4y 4
10. 6x y 14
2x 3y 6
(0, 1)
(1, 5)
9. 2x 3y 3
3y 5 2x
(3, 4)
infinite number
1
y x 2
2
(5, 2)
(3,2)
9. 2x 3y 6
4x 6y 12
6. 2x y 4
y 0.8x 2
8. 2x 3y 0
2x y 8
( 1,1)
(4, 1)
5. y 0.4x
( 1,2)
7. x y 0
5x 2y 3
4. 2x y 7
3x 4y 8
(2, 3)
6. y 3x 1
yx1
5. y 2x 3
y 2x 1
(3, 2)
3. x 2y 8
4x y 5
10. 4x y 3
4x y 1
11. The sum of two numbers is 24. The second number is 6 less
than the first. Write a system of equations and solve it
find the number.
12, 1
no solution
11. The sum of two numbers is 381. Their difference
is 155. Find the two numbers.
x y 24; y x 6; (15, 9)
(113, 268)
12. The theater group sold adult and student tickets for the play.
They sold a total of 560 tickets. Each adult ticket was $8 and
each student ticket was $3.50. The group took in a total of
$3166. How many of each type of ticket were sold for the play?
15. Kerry and Luke biked a total of 18 miles in one weekend.
Kerry biked 4 miles more than Luke. Write a system of equations
and solve it to find how far each boy biked.
x y 18; x 4 y; (7, 11); Luke biked 7 miles, and
292 student tickets; 268 adult tickets
Kerry biked 11 miles
13. The cost of 20 blank recordable CDs and 6 music CDs is $80.70.
The cost of 30 blank recordable CDs and 4 music CDs is $66.30.
Find the cost of each blank recordable CD and each music CD.
blank recordable CD: $0.75; music CD: $10.95
47
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
48
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Reteach
LESSON
11-6 Systems of Equations
Reteach
LESSON
11-6 Systems of Equations (continued)
Two or more equations considered together form a system of equations.
To solve a system of equations, you can use a method of substitution.
Sometimes, you first have to solve one equation for a variable.
Solve the system: y 3x 7
x 2y 4
Solve the system: y 3x
y 5x 20
y 3x 7
3x
3x
Solve the first equation for y.
y 5x 20
3x 5x 20
Use the first equation to
substitute for y in the second equation.
second equation
Replace y with 3x.
2x 20
Solve the resulting equation for x.
Substitute for y in the
second equation.
Solve for x.
Combine like terms.
20
2x
2
2
Divide by 2.
x 10
y 3x
y 3(10) 30
Substitute the x-value into the first
equation to get the corresponding y-value.
x 2y 4
x 2(7 3x) 4
x 14 6x 4
5x 14 4
14
14
5x
10
5
5
Check: Substitute both values in each of the original equations.
y 3x
30 3(10)
30 30 y 5x 20
30 5(10) 20
30 50 20
20 20 Substitute the x-value into
the first equation to get the
corresponding y-value.
x 10 and y 30
So, the solution of the
system is (10, 30).
6x 2x
y 2x
4
16
2(
6x y 16
2
4
4
Solve the resulting equation for x.
)
6(
2
)
4
12 4
So, the ordered pair (2,
the solution of the system.
4. y 2x 0
x 2y 6
16
4)
Substitute the x-value to get the
corresponding y-value.
y 2x
y 2(2)
y 4
Solve the first equation for y.
y 2x 0
is
y
x2
2x
Use the result to substitute for y in
the second equation.
x 2y 6
x 2( 2x ) 6
Substitute the x-value to get the
corresponding y-value.
y 2x
y 2(
y 3x 7
y 3(2) 7
y67
y6676
y1
Solve and check this system.
16
16 16 8x 16
8x
16
8
8
Divide by 5.
Check: Substitute both values in each of the original equations.
y 3x 7
x 2y 4
x 2 and y 1
1 3(2) 7
2 2(1) 4
The solution of the
7 7
4 4
system is (2, 1).
Check both values in each of the
original equations.
Use the first equation to substitute for
y in the second equation.
second equation
Replace y with 7 3x.
Distributive property
Combine like terms.
Subtract 14.
x2
Solve and check this system.
1. y 2x
6x y 16
Subtract 3x.
7 3x
y
Check:
y 2x 0
x 2y 6
Solve the resulting equation for x.
2
)
4
x
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
49
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
66
So, the ordered pair (2, 4)
is the solution of the system.
2
50
Holt Mathematics
Holt Mathematics