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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

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Example Questions

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Example Question #8 : Solve System Of Equations Using Substitution: Ccss.Math.Content.Hsa Rei.C.5

Solve for $\uptext{x}$ and $\uptext{y}$ . Round your answer to the nearest hundredth.

49 x + 10 y = -64

8 x + 30 y = 3

Possible Answers:

x = -8.46 , y = -10.92

x = 17.58 , y = 14.32

x = -10.89 , y = 19.98

x = -1.4 , y = 0.47

x = -7.24 , y = -8.12

Correct answer:

x = -1.4 , y = 0.47

Explanation:

The first step to do is solve for a variable. Let's solve for $\uptext{x}$ first.

49 x + 10 y = -64

Now we subtract 10 y from each side.

49 x + 10 y - 10 y = -64 - 10 y

Now we divide by

$x = - \frac{10 y}{49} - \frac{64}{49}$

Now since we found $\uptext{x}$ , we can plug this into the other equation and find $\uptext{y}$ .

8 x + 30 y = 3

$- \frac{80 y}{49} - \frac{512}{49} + 30 y = 3$

Now we solve for $\uptext{y}$ .

$\frac{1390 y}{49} = 13.448979591836734$

Now we divide by $\frac{1390}{49}$ .

y = 0.47410071942446

Now round to the nearest hundredth.

y= 0.47

Now since we have a value for $\uptext{y}$ , we plug this into the first equation and find $\uptext{x}$ .

49 x + 4.741007194244603 = -64

Now we subtract 4.741007194244603 from each side.

49 x = -68.7410071942446

Now we divide by

x = -1.40287769784173

Now round to the nearest hundredth.

x= -1.4

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Example Question #1 : Solve System Of Equations Using Substitution: Ccss.Math.Content.Hsa Rei.C.5

Solve for $\uptext{x}$ and $\uptext{y}$ . Round your answer to the nearest hundredth.

31 x + 29 y = -83

- 43 x - 12 y = 8

Possible Answers:

x = -18.9 , y = 17.82

x = 0.87 , y = -3.8

x = -11.77 , y = -10.06

x = 17.06 , y = 3.32

x = -2.04 , y = 8.04

Correct answer:

x = 0.87 , y = -3.8

Explanation:

The first step to do is solve for a variable. Let's solve for $\uptext{x}$ first.

31 x + 29 y = -83

Now we subtract 29 y from each side.

31 x + 29 y - 29 y = -83 - 29 y

Now we divide by

$x = - \frac{29 y}{31} - \frac{83}{31}$

Now since we found $\uptext{x}$ , we can plug this into the other equation and find $\uptext{y}$ .

- 43 x - 12 y = 8

$\frac{1247 y}{31} + \frac{3569}{31} + - 12 y = 8$

Now we solve for $\uptext{y}$ .

$\frac{875 y}{31} = -107.12903225806451$

Now we divide by $\frac{875}{31}$ .

y = -3.79542857142857

Now round to the nearest hundredth.

y= -3.8

Now since we have a value for $\uptext{y}$ , we plug this into the first equation and find $\uptext{x}$ .

31 x + -110.06742857142856 = -83

31 x - 110.067428571429 = -83

Now we add 110.06742857142856 to each side.

31 x = 27.067428571428565

Now we divide by

x = 0.873142857142857

Now round to the nearest hundredth.

x= 0.87

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Example Question #10 : Solve System Of Equations Using Substitution: Ccss.Math.Content.Hsa Rei.C.5

Solve for $\uptext{x}$ and $\uptext{y}$ . Round your answer to the nearest hundredth.

- 6 x + 10 y = 80

- 39 x + 13 y = -99

Possible Answers:

x = -7.59 , y = -8.95

x = -15.46 , y = 6.84

x = 6.51 , y = 11.9

x = -3.06 , y = -14.65

x = 5.22 , y = -13.66

Correct answer:

x = 6.51 , y = 11.9

Explanation:

The first step to do is solve for a variable. Let's solve for $\uptext{x}$ first.

- 6 x + 10 y = 80

Now we subtract 10 y from each side.

- 6 x + 10 y - 10 y = 80 - 10 y

Now we divide by

$x = \frac{5 y}{3} - \frac{40}{3}$

Now since we found $\uptext{x}$ , we can plug this into the other equation and find $\uptext{y}$ .

- 39 x + 13 y = -99

- 65 y + 520 + 13 y = -99

Now we solve for $\uptext{y}$ .

- 52 y = -619.0

Now we divide by .

y = 11.9038461538462

Now round to the nearest hundredth.

y= 11.9

Now since we have a value for $\uptext{y}$ , we plug this into the first equation and find $\uptext{x}$ .

- 6 x + 119.03846153846153 = 80

Now we subtract 119.03846153846153 from each side.

- 6 x = -39.03846153846153

Now we divide by

x = 6.50641025641026

Now round to the nearest hundredth.

x= 6.51

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Example Question #11 : Solve System Of Equations Using Substitution: Ccss.Math.Content.Hsa Rei.C.5

Solve for $\uptext{x}$ and $\uptext{y}$ . Round your answer to the nearest hundredth.

29 x + 10 y = -34

23 x + 14 y = 55

Possible Answers:

x = 2.13 , y = 9.2

x = -19.21 , y = 15.81

x = -5.83 , y = 13.51

x = -0.94 , y = -15.77

x = -15.3 , y = 14.36

Correct answer:

x = -5.83 , y = 13.51

Explanation:

The first step to do is solve for a variable. Let's solve for $\uptext{x}$ first.

29 x + 10 y = -34

Now we subtract 10 y from each side.

29 x + 10 y - 10 y = -34 - 10 y

Now we divide by

$x = - \frac{10 y}{29} - \frac{34}{29}$

Now since we found $\uptext{x}$ , we can plug this into the other equation and find $\uptext{y}$ .

23 x + 14 y = 55

$- \frac{230 y}{29} - \frac{782}{29} + 14 y = 55$

Now we solve for $\uptext{y}$ .

$\frac{176 y}{29} = 81.9655172413793$

Now we divide by $\frac{176}{29}$ .

y = 13.5056818181818

Now round to the nearest hundredth.

y= 13.51

Now since we have a value for $\uptext{y}$ , we plug this into the first equation and find $\uptext{x}$ .

29 x + 135.0568181818182 = -34

Now we subtract 135.0568181818182 from each side.

29 x = -169.0568181818182

Now we divide by

x = -5.82954545454546

Now round to the nearest hundredth.

x= -5.83

Report an Error

Example Question #12 : Solve System Of Equations Using Substitution: Ccss.Math.Content.Hsa Rei.C.5

Solve for $\uptext{x}$ and $\uptext{y}$ . Round your answer to the nearest hundredth.

- 37 x + 17 y = 52

23 x - 28 y = 22

Possible Answers:

x = -2.84 , y = -3.12

x = 0.02 , y = -3.25

x = 14.19 , y = 16.1

x = 12.64 , y = -17.63

x = 0.98 , y = -18.97

Correct answer:

x = -2.84 , y = -3.12

Explanation:

The first step to do is solve for a variable. Let's solve for $\uptext{x}$ first.

- 37 x + 17 y = 52

Now we subtract 17 y from each side.

- 37 x + 17 y - 17 y = 52 - 17 y

Now we divide by

$x = \frac{17 y}{37} - \frac{52}{37}$

Now since we found $\uptext{x}$ , we can plug this into the other equation and find $\uptext{y}$ .

23 x - 28 y = 22

$\frac{391 y}{37} - \frac{1196}{37} + - 28 y = 22$

Now we solve for $\uptext{y}$ .

$- \frac{645 y}{37} = 54.32432432432432$

Now we divide by $- \frac{645}{37}$ .

y = -3.11627906976744

Now round to the nearest hundredth.

y= -3.12

Now since we have a value for $\uptext{y}$ , we plug this into the first equation and find $\uptext{x}$ .

- 37 x + -52.97674418604652 = 52

- 37 x - 52.9767441860465 = 52

Now we add 52.97674418604652 to each side.

- 37 x = 104.97674418604652

Now we divide by

x = -2.83720930232558

Now round to the nearest hundredth.

x= -2.84

Report an Error

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

Where do the following lines intersect?

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

Possible Answers:

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

x = -107

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

x = -5

x = 6

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

Where do the following lines intersect?

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

Possible Answers:

x=6

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

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

x=-5

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

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

Where do the following lines intersect?

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

Possible Answers:

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

x = 6

x = -5

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

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

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

Where do the following lines intersect?

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

Possible Answers:

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

x = 6

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

x = -5

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

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

Where do the following lines intersect?

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

Possible Answers:

x = -13

x = 6

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

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

x = -5

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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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 #8 : Solve System Of Equations Using Substitution: Ccss.Math.Content.Hsa Rei.C.5

Example Question #1 : Solve System Of Equations Using Substitution: Ccss.Math.Content.Hsa Rei.C.5

Example Question #10 : Solve System Of Equations Using Substitution: Ccss.Math.Content.Hsa Rei.C.5

Example Question #11 : Solve System Of Equations Using Substitution: Ccss.Math.Content.Hsa Rei.C.5

Example Question #12 : Solve System Of Equations Using Substitution: Ccss.Math.Content.Hsa Rei.C.5

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

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

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

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

Example Question #5 : Solve Systems Of Linear Equations Exactly And Approximately: Ccss.Math.Content.Hsa Rei.C.6

All Common Core: High School - Algebra Resources

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