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Common Core: High School - Algebra : High School: Algebra

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 #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:

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

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

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

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

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

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 #622 : High School: Algebra

Where do the following equations intersect?

y = - 23 x - 30

y = 4 x - 13

Possible Answers:

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

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

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

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

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

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 #1 : 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:

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

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

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

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

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

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.

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

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

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

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Example Question #624 : High School: Algebra

Where do the following equations intersect?

y = - 29 x - 22

y = - x - 9

Possible Answers:

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

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

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

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

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

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.

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

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

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

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Example Question #625 : High School: Algebra

Where do the following equations intersect?

y = 29 x + 30

y = - 41 x + 33

Possible Answers:

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

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

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

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

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

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.

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

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

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

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Example Question #626 : High School: Algebra

Where do the following equations intersect?

y = - 10 x + 41

y = 7 x + 7

Possible Answers:

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

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

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

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

$\left( 2 , 21 \right)$

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

Report an Error

Example Question #627 : High School: Algebra

Where do the following equations intersect?

y = - 4 x - 12

y = - 42 x + 30

Possible Answers:

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

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

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

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

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

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.

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

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

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

Report an Error

Example Question #171 : Reasoning With Equations & Inequalities

Where do the following equations intersect?

y = 3 x - 20

y = 42

Possible Answers:

$\left( \infty , 42 \right)$

$\left( \frac{23}{42} , 25 \right)$

$\left( \frac{23}{42} , \frac{2}{3} \right)$

$\left( \frac{23}{42} , 42 \right)$

$\left( \frac{62}{3} , 42 \right)$

Correct answer:

$\left( \frac{62}{3} , 42 \right)$

Explanation:

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

3 x - 20 = 42

Now we add to each side.

3 x = 62

Now we divide by on each side.

$x = \frac{62}{3}$

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

$y = 3 \cdot \frac{62}{3} -20$

y = 62 -20

y = 42

Report an Error

Example Question #172 : Reasoning With Equations & Inequalities

Where do the following equations intersect?

y = 42 x - 2

y = - 38 x + 27

Possible Answers:

$\left( \frac{29}{80} , \frac{529}{40} \right)$

$\left( \frac{44}{65} , 29 \right)$

$\left( - \frac{21}{19} , \frac{529}{40} \right)$

$\left( \frac{44}{65} , \frac{529}{40} \right)$

$\left( \frac{44}{65} , - \frac{131}{80} \right)$

Correct answer:

$\left( \frac{29}{80} , \frac{529}{40} \right)$

Explanation:

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

42 x - 2 = - 38 x + 27

Now we add to each side.

42 x = - 38 x + 29

Now we add 38 x to each side.

80 x = 29

Now we divide by on each side.

$x = \frac{29}{80}$

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

$y = 42 \cdot \frac{29}{80} -2$

$y = \frac{609}{40} -2$

$y = \frac{529}{40}$

Report an Error

Example Question #173 : Reasoning With Equations & Inequalities

Where do the following equations intersect?

y = 41 x + 7

y = - x + 27

Possible Answers:

$\left( \frac{17}{14} , 74 \right)$

$\left( \frac{17}{14} , \frac{557}{21} \right)$

$\left( -41 , \frac{557}{21} \right)$

$\left( \frac{17}{14} , \frac{157}{21} \right)$

$\left( \frac{10}{21} , \frac{557}{21} \right)$

Correct answer:

$\left( \frac{10}{21} , \frac{557}{21} \right)$

Explanation:

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

41 x + 7 = - x + 27

Now we subtract from each side.

41 x = - x + 20

Now we add to each side.

42 x = 20

Now we divide by on each side.

$x = \frac{10}{21}$

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

$y = 41 \cdot \frac{10}{21} + 7$

$y = \frac{410}{21} + 7$

$y = \frac{557}{21}$

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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

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Common Core: High School - Algebra : High School: Algebra

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

All Common Core: High School - Algebra Resources

Example Questions

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

Example Question #622 : High School: Algebra

Example Question #1 : Use Graph Points To Approximate Solutions: Ccss.Math.Content.Hsa Rei.D.11

Example Question #624 : High School: Algebra

Example Question #625 : High School: Algebra

Example Question #626 : High School: Algebra

Example Question #627 : High School: Algebra

Example Question #171 : Reasoning With Equations & Inequalities

Example Question #172 : Reasoning With Equations & Inequalities

Example Question #173 : Reasoning With Equations & Inequalities

All Common Core: High School - Algebra Resources

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