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Common Core: High School - Algebra : Reasoning with Equations & Inequalities

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

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All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #161 : Reasoning With Equations & Inequalities

Where do the following equations intersect?

y = - 45 x + 19

y = 43 x - 4

Possible Answers:

$\left( \frac{64}{47} , \frac{1695}{88} \right)$

$\left( \frac{64}{47} , \frac{637}{88} \right)$

$\left( - \frac{45}{43} , \frac{637}{88} \right)$

$\left( \frac{64}{47} , 13 \right)$

$\left( \frac{23}{88} , \frac{637}{88} \right)$

Correct answer:

$\left( \frac{23}{88} , \frac{637}{88} \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

- 45 x + 19 = 43 x - 4

- 45 x = 43 x - 23

- 88 x = -23

$x = \frac{23}{88}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -45 \cdot \frac{23}{88} + 19$

$y = - \frac{1035}{88} + 19$

$y = \frac{637}{88}$

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Example Question #162 : Reasoning With Equations & Inequalities

Where do the following equations intersect?

y = 22 x - 47

y = - 44 x + 4

Possible Answers:

$\left( \frac{23}{16} , - \frac{1017}{22} \right)$

$\left( \frac{23}{16} , -30 \right)$

$\left( \frac{17}{22} , -30 \right)$

$\left( - \frac{1}{2} , -30 \right)$

$\left( \frac{23}{16} , -65 \right)$

Correct answer:

$\left( \frac{17}{22} , -30 \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}.$

22 x - 47 = - 44 x + 4

22 x = - 44 x + 51

66 x = 51

$x = \frac{17}{22}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = 22 \cdot \frac{17}{22} -47$

y = 17 -47

y = -30

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Example Question #3 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Where do the following equations intersect?

y = 49 x + 17

y = - 40 x - 23

Possible Answers:

$\left( - \frac{40}{89} , - \frac{447}{89} \right)$

$\left( - \frac{49}{40} , - \frac{447}{89} \right)$

$\left( \frac{32}{17} , - \frac{447}{89} \right)$

$\left( \frac{32}{17} , \frac{1473}{89} \right)$

$\left( \frac{32}{17} , 3 \right)$

Correct answer:

$\left( - \frac{40}{89} , - \frac{447}{89} \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}.$

Subtract from both sides:

49 x + 17 = - 40 x - 23

Add 40x to both sides:

49 x = - 40 x - 40

Divide both sides by $89\textup:$

89 x = -40

$x = - \frac{40}{89}$

Now plug this $\uptext{x}$ value into one of the equations to solve for the $\uptext{y}$ value.

y = 49 x + 17

$y = 49 \cdot - \frac{40}{89} + 17$

Multiply $\frac{49}{1}$ by $-\frac{40}{89}\textup:$

$y = - \frac{1960}{89} + 17$

Make fractions with common denominators:

$\frac{17}{1}=\frac{1513}{89}$

Add fractions:

$y = - \frac{1960}{89} + \frac{1513}{89}$

$y = - \frac{447}{89}$

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Example Question #4 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Where do the following equations intersect?

y = 16 x + 22

y = - 10 x + 30

Possible Answers:

$\left( - \frac{3}{20} , \frac{350}{13} \right)$

$\left( - \frac{3}{20} , \frac{290}{13} \right)$

$\left( \frac{4}{13} , \frac{350}{13} \right)$

$\left( - \frac{3}{20} , 58 \right)$

$\left( - \frac{8}{5} , \frac{350}{13} \right)$

Correct answer:

$\left( \frac{4}{13} , \frac{350}{13} \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

16 x + 22 = - 10 x + 30

Now we subtract from each side.

16 x = - 10 x + 8

Now we add 10 x to each side.

26 x = 8

Now we divide by on each side.

$x = \frac{4}{13}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = 16 \cdot \frac{4}{13} + 22$

$y = \frac{64}{13} + 22$

$y = \frac{350}{13}$

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Example Question #2 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Where do the following equations intersect?

y = - 23 x - 30

y = 4 x - 13

Possible Answers:

$\left( - \frac{7}{17} , - \frac{419}{27} \right)$

$\left( - \frac{7}{17} , - \frac{827}{27} \right)$

$\left( - \frac{23}{4} , - \frac{419}{27} \right)$

$\left( - \frac{17}{27} , - \frac{419}{27} \right)$

$\left( - \frac{7}{17} , -62 \right)$

Correct answer:

$\left( - \frac{17}{27} , - \frac{419}{27} \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

- 23 x - 30 = 4 x - 13

Now we add to each side.

- 23 x = 4 x + 17

Now we subtract 4 x from each side.

- 27 x = 17

Now we divide by on each side.

$x = - \frac{17}{27}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -23 \cdot - \frac{17}{27} -30$

$y = \frac{391}{27} -30$

$y = - \frac{419}{27}$

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Example Question #3 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Where do the following equations intersect?

y = - 4 x + 20

y = 12 x - 35

Possible Answers:

$\left( \frac{24}{47} , -7 \right)$

$\left( - \frac{1}{3} , \frac{25}{4} \right)$

$\left( \frac{24}{47} , \frac{25}{4} \right)$

$\left( \frac{24}{47} , \frac{375}{16} \right)$

$\left( \frac{55}{16} , \frac{25}{4} \right)$

Correct answer:

$\left( \frac{55}{16} , \frac{25}{4} \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

- 4 x + 20 = 12 x - 35

Now we subtract from each side.

- 4 x = 12 x - 55

Now we subtract 12 x from each side.

- 16 x = -55

Now we divide by on each side.

$x = \frac{55}{16}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -4 \cdot \frac{55}{16} + 20$

$y = - \frac{55}{4} + 20$

$y = \frac{25}{4}$

Report an Error

Example Question #4 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Where do the following equations intersect?

y = - 29 x - 22

y = - x - 9

Possible Answers:

$\left( \frac{7}{8} , - \frac{629}{28} \right)$

$\left( \frac{7}{8} , -61 \right)$

$\left( - \frac{13}{28} , - \frac{239}{28} \right)$

$\left( \frac{7}{8} , - \frac{239}{28} \right)$

$\left( 29 , - \frac{239}{28} \right)$

Correct answer:

$\left( - \frac{13}{28} , - \frac{239}{28} \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

- 29 x - 22 = - x - 9

Now we add to each side.

- 29 x = - x + 13

Now we add to each side.

- 28 x = 13

Now we divide by on each side.

$x = - \frac{13}{28}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -29 \cdot - \frac{13}{28} -22$

$y = \frac{377}{28} -22$

$y = - \frac{239}{28}$

Report an Error

Example Question #5 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Where do the following equations intersect?

y = 29 x + 30

y = - 41 x + 33

Possible Answers:

$\left( - \frac{29}{41} , \frac{2187}{70} \right)$

$\left( \frac{3}{70} , \frac{2187}{70} \right)$

$\left( - \frac{1}{74} , 51 \right)$

$\left( - \frac{1}{74} , \frac{2103}{70} \right)$

$\left( - \frac{1}{74} , \frac{2187}{70} \right)$

Correct answer:

$\left( \frac{3}{70} , \frac{2187}{70} \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

29 x + 30 = - 41 x + 33

Now we subtract from each side.

29 x = - 41 x + 3

Now we add 41 x to each side.

70 x = 3

Now we divide by on each side.

$x = \frac{3}{70}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = 29 \cdot \frac{3}{70} + 30$

$y = \frac{87}{70} + 30$

$y = \frac{2187}{70}$

Report an Error

Example Question #6 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Where do the following equations intersect?

y = - 10 x + 41

y = 7 x + 7

Possible Answers:

$\left( -\infty , 21 \right)$

$\left( -\infty , 43 \right)$

$\left( -\infty , 45 \right)$

$\left( 2 , 21 \right)$

$\left( - \frac{10}{7} , 21 \right)$

Correct answer:

$\left( 2 , 21 \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

- 10 x + 41 = 7 x + 7

Now we subtract from each side.

- 10 x = 7 x - 34

Now we subtract 7 x from each side.

- 17 x = -34

Now we divide by on each side.

x = 2

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -10 \cdot 2 + 41$

y = -20 + 41

y = 21

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Example Question #7 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Where do the following equations intersect?

y = - 4 x - 12

y = - 42 x + 30

Possible Answers:

$\left( \frac{21}{19} , - \frac{312}{19} \right)$

$\left( \frac{1}{9} , - \frac{207}{19} \right)$

$\left( \frac{1}{9} , -28 \right)$

$\left( \frac{2}{21} , - \frac{312}{19} \right)$

$\left( \frac{1}{9} , - \frac{312}{19} \right)$

Correct answer:

$\left( \frac{21}{19} , - \frac{312}{19} \right)$

Explanation:

To figure out where these equations intersect, we need to set them equal to each other and solve for $\uptext{x}$ .

- 4 x - 12 = - 42 x + 30

Now we add to each side.

- 4 x = - 42 x + 42

Now we add 42 x to each side.

38 x = 42

Now we divide by on each side.

$x = \frac{21}{19}$

Now we simply plug this $\uptext{x}$ value into one of the equations to get the $\uptext{y}$ value.

$y = -4 \cdot \frac{21}{19} -12$

$y = - \frac{84}{19} -12$

$y = - \frac{312}{19}$

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All Common Core: High School - Algebra Resources

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Common Core: High School - Algebra : Reasoning with Equations & Inequalities

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

All Common Core: High School - Algebra Resources

Example Questions

Example Question #161 : Reasoning With Equations & Inequalities

Example Question #162 : Reasoning With Equations & Inequalities

Example Question #3 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Example Question #4 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Example Question #2 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Example Question #3 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Example Question #4 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Example Question #5 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Example Question #6 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Example Question #7 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

All Common Core: High School - Algebra Resources

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