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

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Example Questions

Example Question #1 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

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

Possible Answers:

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

\displaystyle x = 6

\displaystyle x = -5

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

\displaystyle x = -107

Correct answer:

\displaystyle 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 .

\displaystyle 39 x - 23 = 41 x + 84

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

\displaystyle 39 x = 41 x + 107

\displaystyle 39 x - 41 x = 41 x + 107 - 41 x

\displaystyle - 2 x = 107

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

 

Example Question #2 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

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

Possible Answers:

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

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

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

\displaystyle x=-5

\displaystyle x=6

Correct answer:

\displaystyle 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 .

\displaystyle 22 x - 27 = 2 x + 95

\displaystyle 22 x - 27 + 27 = 2 x + 95 + 2722 x = 2 x + 122

\displaystyle 22 x - 2 x = 2 x + 122 - 2 x

\displaystyle 20 x = 122

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

 

Example Question #78 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

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

Possible Answers:

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

\displaystyle x = -5

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

\displaystyle x = 6

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

Correct answer:

\displaystyle 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 .

\displaystyle 45 x - 60 = 15 x - 99

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

\displaystyle 45 x = 15 x - 39

\displaystyle 45 x - 15 x = 15 x - 39 - 15 x

\displaystyle 30 x = -39

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

Example Question #79 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

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

Possible Answers:

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

\displaystyle x = -5

\displaystyle x = 6

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

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

Correct answer:

\displaystyle 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 .

\displaystyle 29 x + 24 = 21 x - 6

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

\displaystyle 29 x = 21 x - 30

\displaystyle 29 x - 21 x = 21 x - 30 - 21 x

\displaystyle 8 x = -30

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

Example Question #531 : High School: Algebra

Where do the following lines intersect?

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

Possible Answers:

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

\displaystyle x = -13

\displaystyle x = 6

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

\displaystyle x = -5

Correct answer:

\displaystyle 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 .

\displaystyle 39 x + 99 = 27 x + 21

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

\displaystyle 39 x = 27 x - 78

\displaystyle 39 x - 27 x = 27 x - 78 - 27 x

\displaystyle 12 x = -78

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

Example Question #1 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

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

Possible Answers:

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

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

\displaystyle x = -5

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

\displaystyle x = 6

Correct answer:

\displaystyle 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 .

\displaystyle 41 x + 85 = 19 x + 84

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

\displaystyle 41 x = 19 x - 1

\displaystyle 41 x - 19 x = 19 x - 1 - 19 x

\displaystyle 22 x = -1

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

 

Example Question #3 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

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

Possible Answers:

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

\displaystyle x = -5

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

\displaystyle x = 6

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

Correct answer:

\displaystyle 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 .

\displaystyle 16 x + 86 = 2 x - 78

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

\displaystyle 16 x = 2 x - 164

\displaystyle 16 x - 2 x = 2 x - 164 - 2 x

\displaystyle 14 x = -164

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

Example Question #3 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

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

Possible Answers:

\displaystyle x = -7

\displaystyle x = -5

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

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

\displaystyle x = 6

Correct answer:

\displaystyle 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 .

\displaystyle 6 x - 13 = 22 x + 43

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

\displaystyle 6 x = 22 x + 56

\displaystyle 6 x - 22 x = 22 x + 56 - 22 x

\displaystyle - 16 x = 56

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

Example Question #4 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

Where do the following lines intersect?

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

Possible Answers:

\displaystyle - \frac{41}{16}

\displaystyle x = 6

\displaystyle x = -5

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

\displaystyle \frac{41}{8}

Correct answer:

\displaystyle 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 .

\displaystyle 11 x + 72 = 27 x + 31

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

\displaystyle 11 x = 27 x - 41

\displaystyle 11 x - 27 x = 27 x - 41 - 27 x

\displaystyle - 16 x = -41

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

 

Example Question #81 : Reasoning With Equations & Inequalities

Where do the following lines intersect?

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

Possible Answers:

\displaystyle x = 10

\displaystyle x = 6

\displaystyle x = -20

\displaystyle x = -5

\displaystyle x = -10

Correct answer:

\displaystyle 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 .

\displaystyle 16 x - 39 = 29 x + 91

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

\displaystyle 16 x = 29 x + 130

\displaystyle 16 x - 29 x = 29 x + 130 - 29 x

\displaystyle - 13 x = 130

\displaystyle x = -10

 

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