Lesson 6.1 Unit 6 Homework Key - MMS 8th Grade Math

Lesson 6.1

Unit 6 Homework Key

Graph the following linear equations using slope-intercept form.

1. = 2 + 1

2. = 3 - 4

3.

= 2 + 5

3

4. = -2 + 1

5. = -3 - 2

6.

= - 1 + 5

3

7.

=

2

5

-

2

8.

=

- 3

4

-1

9. = -4

1

10. 2 + = 2

11. -3 + = 4

12. 4 + = -5

13. 4 + 2 = 6

14. -6 + 3 = -9

15. + 3 = 6

16. -2 + 3 = 12

17. 4 - 2 = 8

18. -2 - 3 = -9

2

Lesson 6.2

Graph the following systems of equations and estimate the solution from the graph.

1.

= + 1 = - 3 + 6

(, )

2

2. = 2 + 8 (-, )

= + 6

3.

= -2 + 3

=

1 2

-

4

(. , -. )

4.

= 2 + 3

(. , )

= 4

5. 3 = + 9 (-, )

2 = -4 - 8

6. 4 + 2 = 6 (, )

-6 + 2 = 6

3

7.

3 = 6

(, )

2 = - + 12

8. - + 3 = -18 (. , -. )

+ 2 = -4

9.

= - = + 2

(-, )

10. + = 6 =

(, )

11. 4 + 3 = 24 (, )

2 - 3 = -6

12.

+ = 2 2 - = 10

(-, )

4

13. - 2 = 2 (, )

3 + = 6

14. = -4

(, -)

= -3 - 4

15. = + 3 (-. , . )

3 + = 6

16. + 5 = -5 (. , -. )

3 - 2 = 8

17. - + = -1

- = 1 Infinite Solutions

18.

4 = 2 - 10 2 = 4 + 4

No Solution

5

Lesson 6.3

Solve the following systems using the substitution method.

1.

2 + 8 = 12

- 2 = 0

(2, 1)

2. + = 7 2 + = 5

(-2, 9)

3.

= 5

2 - = 9

(7, 5)

4.

= - 1 + 1

2

2 + 3 = 6

(6, -2)

5.

2 + = -16

- 2 = -28

(-12, 8)

6. 4 = 8 2 + 5 = 11

(1 , 2)

2

7.

+ = 2

-2 + 4 = -19 (4.5, -2.5)

8. + 2 = 4 3 - 4 = -3

(1, 1.5)

9.

2 + = 4

2 = -4 + 8

10. + = 2

+ = 5

11. = 3 3 + 3 = 4

(1 , 1)

3

13. - 3 = 0 1 + = 2

3

(3, 1)

12. = 2 + 3 = 4 - 1

(2, 7)

14.

2 - 1 = -9

3

-3 + = 15

(-4, 3)

6

15. = 2 2 + = 4

(2, 0)

17. 3 = 2

2

= - 1

(4, 3)

16. 4 = 3 + 3 = 2

(2, 5)

3

18. - 2 = -1 3 = + 4

(5, 3)

19. + 2 = 0 3 + 4 = 4

(4, -2)

20. 2 = -6 + 2 = -1

(5, -3)

21. - 4 = 1 2 - 8 = 2

22. - 2 = 3

4 - 8 = 12

23. = 0 3 - 6 = 12

(0, -2)

24. = 2 - 3 = 2 + 4

25. 2 - 3 = -24 + 1 = -5

4

(-6, 4)

26.

2 - 2 = 12

3

= -2 - 2

(6, -4)

27. + = 6 2 = -2 + 2

28. + 2 = 7 2 - 8 = 8

(6, 1)

2

29. 2 = 6 - 14 3 - = 7

30. = - + 3

2 + 2 = 4

7

Write and solve a system of equations using any method (graphing, elimination, or substitution) for each of the following situations. 31. Leonard sells small watermelons for $7 each and large watermelons for $10 each. One day the number of small watermelons he sold was fifteen more than the number of large watermelons, and he made a total of $394. How many small and how many large watermelons did he sell?

32 small watermelons and 17 large watermelons

32. The perimeter of a rectangle is 28 cm. The length of the rectangle is 2 cm more than twice the width. Find the dimensions of the rectangle.

Length = 10 ; width= 4

33. The sum of Julian's and Kira's age is 58. Kira is fourteen less than twice as old as Julian. What are their ages? Julian is 24 years old and Kira is 34 years old

34. A 3% solution of sulfuric acid was mixed with an 18% solution of sulfuric acid to produce an 8% solution. How much 3% solution and how much 18% solution were used to produce 15 L of 8% solution?

10 L of the 3% solution and 5 L of the 18% solution

35. Supplementary angles are two angles whose measures have the sum of 180 degrees. Angles X and Y are supplementary, and the measure of angle X is 24 degrees greater than the measure of angle Y. Find the measures of angles X and Y.

Measure of angle = 102? ; measure of angle = 78?

36. At the end of the 2000 baseball season, the New York Yankees and the Cincinnati Reds had won a total of 31 World Series. The Yankees had won 5.2 times as many World Series as the Reds. How many World Series did each team win?

Yankees won 26 World Series and Reds won 5 World Series

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