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Common Core: High School - Algebra : Solve Systems of Linear Equations Exactly and Approximately: CCSS.Math.Content.HSA-REI.C.6

Study concepts, example questions & explanations for Common Core: High School - Algebra

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All Common Core: High School - Algebra Resources

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Example Questions

Example Question #71 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 39 x - 23 and y = 41 x + 84

Possible Answers:

$x = \frac{107}{2}$

x = -5

x = -107

x = 6

$x = - \frac{107}{2}$

Correct answer:

$x = - \frac{107}{2}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

39 x - 23 = 41 x + 84

39 x - 23 + 23 = 41 x + 84 + 23

39 x = 41 x + 107

39 x - 41 x = 41 x + 107 - 41 x

- 2 x = 107

$x = - \frac{107}{2}$

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Example Question #72 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 22 x - 27 and y = 2 x + 95

Possible Answers:

x=-5

$x=\frac{61}{5}$

$x=\frac{61}{10}$

x=6

$x=- \frac{61}{10}$

Correct answer:

$x=\frac{61}{10}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

22 x - 27 = 2 x + 95

22 x - 27 + 27 = 2 x + 95 + 27 22 x = 2 x + 122

22 x - 2 x = 2 x + 122 - 2 x

20 x = 122

$x = \frac{61}{10}$

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Example Question #73 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 45 x - 60 and y = 15 x - 99

Possible Answers:

$x = \frac{13}{10}$

x = 6

$x = - \frac{13}{5}$

$x = - \frac{13}{10}$

x = -5

Correct answer:

$x = - \frac{13}{10}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

45 x - 60 = 15 x - 99

45 x - 60 + 60 = 15 x - 99 + 60

45 x = 15 x - 39

45 x - 15 x = 15 x - 39 - 15 x

30 x = -39

$x = - \frac{13}{10}$

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Example Question #74 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 29 x + 24 and y = 21 x - 6

Possible Answers:

x = -5

$x = - \frac{15}{4}$

x = 6

$x = - \frac{15}{2}$

$x = \frac{15}{4}$

Correct answer:

$x = - \frac{15}{4}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

29 x + 24 = 21 x - 6

29 x + 24 - 24 = 21 x - 6 - 24

29 x = 21 x - 30

29 x - 21 x = 21 x - 30 - 21 x

8 x = -30

$x = - \frac{15}{4}$

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Example Question #75 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 39 x + 99 and y = 27 x + 21

Possible Answers:

x = -13

$x = - \frac{13}{2}$

x = -5

$x = \frac{13}{2}$

x = 6

Correct answer:

$x = - \frac{13}{2}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

39 x + 99 = 27 x + 21

39 x + 99 - 99 = 27 x + 21 - 99

39 x = 27 x - 78

39 x - 27 x = 27 x - 78 - 27 x

12 x = -78

$x = - \frac{13}{2}$

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Example Question #81 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 41 x + 85 and y = 19 x + 84

Possible Answers:

$x = \frac{1}{22}$

x = -5

x = 6

$x = - \frac{1}{11}$

$x = - \frac{1}{22}$

Correct answer:

$x = - \frac{1}{22}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

41 x + 85 = 19 x + 84

41 x + 85 - 85 = 19 x + 84 - 85

41 x = 19 x - 1

41 x - 19 x = 19 x - 1 - 19 x

22 x = -1

$x = - \frac{1}{22}$

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Example Question #82 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 16 x + 86 and y = 2 x - 78

Possible Answers:

$x = - \frac{164}{7}$

$x = - \frac{82}{7}$

x = -5

x = 6

$x = \frac{82}{7}$

Correct answer:

$x = - \frac{82}{7}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

16 x + 86 = 2 x - 78

16 x + 86 - 86 = 2 x - 78 - 86

16 x = 2 x - 164

16 x - 2 x = 2 x - 164 - 2 x

14 x = -164

$x = - \frac{82}{7}$

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Example Question #83 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 6 x - 13 and y = 22 x + 43

Possible Answers:

x = -5

x = 6

$x = - \frac{7}{2}$

$x = \frac{7}{2}$

x = -7

Correct answer:

$x = - \frac{7}{2}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

6 x - 13 = 22 x + 43

6 x - 13 + 13 = 22 x + 43 + 13

6 x = 22 x + 56

6 x - 22 x = 22 x + 56 - 22 x

- 16 x = 56

$x = - \frac{7}{2}$

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Example Question #84 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 11 x + 72 and y = 27 x + 31

Possible Answers:

$x = \frac{41}{16}$

x = -5

$- \frac{41}{16}$

x = 6

$\frac{41}{8}$

Correct answer:

$x = \frac{41}{16}$

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

11 x + 72 = 27 x + 31

11 x + 72 - 72 = 27 x + 31 - 72

11 x = 27 x - 41

11 x - 27 x = 27 x - 41 - 27 x

- 16 x = -41

$x = \frac{41}{16}$

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Example Question #85 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

y = 16 x - 39 and y = 29 x + 91

Possible Answers:

x = 6

x = -20

x = 10

x = -5

x = -10

Correct answer:

x = -10

Explanation:

In order to figure out this problem, we need to set each of the equations equal to each other, and solve for $\uptext{x}$ .

16 x - 39 = 29 x + 91

16 x - 39 + 39 = 29 x + 91 + 39

16 x = 29 x + 130

16 x - 29 x = 29 x + 130 - 29 x

- 13 x = 130

x = -10

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All Common Core: High School - Algebra Resources

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Common Core: High School - Algebra : Solve Systems of Linear Equations Exactly and Approximately: CCSS.Math.Content.HSA-REI.C.6

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #71 : Reasoning With Equations & Inequalities

Example Question #72 : Reasoning With Equations & Inequalities

Example Question #73 : Reasoning With Equations & Inequalities

Example Question #74 : Reasoning With Equations & Inequalities

Example Question #75 : Reasoning With Equations & Inequalities

Example Question #81 : Reasoning With Equations & Inequalities

Example Question #82 : Reasoning With Equations & Inequalities

Example Question #83 : Reasoning With Equations & Inequalities

Example Question #84 : Reasoning With Equations & Inequalities

Example Question #85 : Reasoning With Equations & Inequalities

All Common Core: High School - Algebra Resources

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