Common Core: High School - Algebra : Solve System of Equations Using Substitution: CCSS.Math.Content.HSA-REI.C.5

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Example Questions

Example Question #63 : Reasoning With Equations & Inequalities

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

\displaystyle x + 6 y = 13

\displaystyle 14 x - 3 y = -46

Possible Answers:

\displaystyle x = 13.74 , y = -1.12

\displaystyle x = -2.72 , y = 2.62

\displaystyle x = 18.87 , y = -14.64

\displaystyle x = 19.75 , y = 2.55

\displaystyle x = -0.83 , y = 17.03

Correct answer:

\displaystyle x = -2.72 , y = 2.62

Explanation:

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

\displaystyle x + 6 y = 13

Now we subtract \displaystyle 6 y from each side.

\displaystyle x + 6 y - 6 y = 13 - 6 y

Now we divide by \displaystyle 1

\displaystyle x = - 6 y + 13

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

\displaystyle 14 x - 3 y = -46

\displaystyle - 84 y + 182 + - 3 y = -46

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

\displaystyle - 87 y = -228.0

Now we divide by \displaystyle -87.

\displaystyle y = 2.62068965517241

Now round to the nearest hundredth.

\displaystyle y= 2.62

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

\displaystyle x + 15.724137931034482 = 13

Now we subtract \displaystyle 15.724137931034482 from each side.

\displaystyle x = -2.724137931034482

Now we divide by \displaystyle 1

\displaystyle x = -2.72413793103448

 

Now round to the nearest hundredth.

\displaystyle x= -2.72

Example Question #64 : Reasoning With Equations & Inequalities

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

\displaystyle - 3 x + 14 y = -95

\displaystyle 38 x + 13 y = 28

Possible Answers:

\displaystyle x = -1.24 , y = 9.2

\displaystyle x = -0.9 , y = -17.17

\displaystyle x = 2.85 , y = -6.18

\displaystyle x = -8.58 , y = -15.58

\displaystyle x = -19.72 , y = -9.45

Correct answer:

\displaystyle x = 2.85 , y = -6.18

Explanation:

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

\displaystyle - 3 x + 14 y = -95

Now we subtract \displaystyle 14 y from each side.

\displaystyle - 3 x + 14 y - 14 y = -95 - 14 y

Now we divide by \displaystyle -3

\displaystyle x = \frac{14 y}{3} + \frac{95}{3}

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

\displaystyle 38 x + 13 y = 28

\displaystyle \frac{532 y}{3} + \frac{3610}{3} + 13 y = 28

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

\displaystyle \frac{571 y}{3} = -1175.3333333333333

Now we divide by \displaystyle \frac{571}{3}

\displaystyle y = -6.17513134851138

Now round to the nearest hundredth.

\displaystyle y= -6.18

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

\displaystyle - 3 x + -86.45183887915935 = -95

\displaystyle - 3 x - 86.4518388791594 = -95

Now we add \displaystyle 86.45183887915935 to each side.

\displaystyle - 3 x = -8.548161120840646

Now we divide by \displaystyle -3

\displaystyle x = 2.84938704028022

 

Now round to the nearest hundredth.

\displaystyle x= 2.85

Example Question #65 : Reasoning With Equations & Inequalities

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

\displaystyle 16 x + 42 y = -94

\displaystyle 14 x - 26 y = -68

Possible Answers:

\displaystyle x = 0.66 , y = -6.54

\displaystyle x = 11.51 , y = -7.77

\displaystyle x = -5.28 , y = -0.23

\displaystyle x = -16.26 , y = 14.15

\displaystyle x = -19.6 , y = 12.87

Correct answer:

\displaystyle x = -5.28 , y = -0.23

Explanation:

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

\displaystyle 16 x + 42 y = -94

Now we subtract \displaystyle 42 y from each side.

\displaystyle 16 x + 42 y - 42 y = -94 - 42 y

Now we divide by \displaystyle 16

\displaystyle x = - \frac{21 y}{8} - \frac{47}{8}

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

\displaystyle 14 x - 26 y = -68

\displaystyle - \frac{147 y}{4} - \frac{329}{4} + - 26 y = -68

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

\displaystyle - \frac{251 y}{4} = 14.25

Now we divide by \displaystyle - \frac{251}{4}.

\displaystyle y = -0.227091633466135

Now round to the nearest hundredth.

\displaystyle y= -0.23

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

\displaystyle 16 x + -9.53784860557769 = -94

Now we add \displaystyle 9.53784860557769 to each side.

\displaystyle 16 x = -84.4621513944223

Now we divide by \displaystyle 16

\displaystyle x = -5.27888446215139

 

Now round to the nearest hundredth.

\displaystyle x= -5.28

Example Question #66 : Reasoning With Equations & Inequalities

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

\displaystyle 5 x + 5 y = 80

\displaystyle - 39 x + 8 y = -60

Possible Answers:

\displaystyle x = -1.79 , y = -9.08

\displaystyle x = -11.68 , y = -2.49

\displaystyle x = -1.9 , y = -12.84

\displaystyle x = 17.0 , y = 18.64

\displaystyle x = 4.0 , y = 12.0

Correct answer:

\displaystyle x = 4.0 , y = 12.0

Explanation:

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

\displaystyle 5 x + 5 y = 80

Now we subtract \displaystyle 5 y from each side.

\displaystyle 5 x + 5 y - 5 y = 80 - 5 y

Now we divide by \displaystyle 5

\displaystyle x = - y + 16

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

\displaystyle - 39 x + 8 y = -60

\displaystyle 39 y - 624 + 8 y = -60

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

\displaystyle 47 y = 564.0

Now we divide by \displaystyle 47 .

\displaystyle y = 12.0

Now round to the nearest hundredth.

\displaystyle y= 12.0

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

\displaystyle 5 x + 60.0 = 80

Now we subtract \displaystyle 60.0 from each side.

\displaystyle 5 x = 20.0

Now we divide by \displaystyle 5

\displaystyle x = 4.0

 

Now round to the nearest hundredth.

\displaystyle x= 4.0

Example Question #67 : Reasoning With Equations & Inequalities

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

\displaystyle 22 x + 11 y = 98

\displaystyle 18 x + 46 y = -57

Possible Answers:

\displaystyle x = -10.41 , y = -4.61

\displaystyle x = -7.34 , y = -17.71

\displaystyle x = -13.59 , y = 14.39

\displaystyle x = 6.31 , y = -3.71

\displaystyle x = -9.08 , y = -13.49

Correct answer:

\displaystyle x = 6.31 , y = -3.71

Explanation:

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

\displaystyle 22 x + 11 y = 98

Now we subtract \displaystyle 11 y from each side.

\displaystyle 22 x + 11 y - 11 y = 98 - 11 y

Now we divide by \displaystyle 22

\displaystyle x = - \frac{y}{2} + \frac{49}{11}

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

\displaystyle 18 x + 46 y = -57

\displaystyle - 9 y + \frac{882}{11} + 46 y = -57

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

\displaystyle 37 y = -137.1818181818182

Now we divide by \displaystyle 37.

\displaystyle y = -3.70761670761671

Now round to the nearest hundredth.

\displaystyle y= -3.71

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

\displaystyle 22 x + -40.78378378378378 = 98

\displaystyle 22 x - 40.7837837837838 = 98

Now we add \displaystyle 40.78378378378378 on each side.

\displaystyle 22 x = 138.78378378378378

Now we divide by \displaystyle 22

\displaystyle x = 6.30835380835381

 

Now round to the nearest hundredth.

\displaystyle x= 6.31

Example Question #68 : Reasoning With Equations & Inequalities

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

\displaystyle 2 x + 45 y = -15

\displaystyle 39 x - 22 y = 64

Possible Answers:

\displaystyle x = 7.4 , y = -15.52

\displaystyle x = 19.33 , y = -12.72

\displaystyle x = 0.31 , y = -7.41

\displaystyle x = -6.91 , y = -4.18

\displaystyle x = 1.42 , y = -0.4

Correct answer:

\displaystyle x = 1.42 , y = -0.4

Explanation:

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

\displaystyle 2 x + 45 y = -15

Now we subtract \displaystyle 45 y from each side.

\displaystyle 2 x + 45 y - 45 y = -15 - 45 y

Now we divide by \displaystyle 2

\displaystyle x = - \frac{45 y}{2} - \frac{15}{2}

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

\displaystyle 39 x - 22 y = 64

\displaystyle - \frac{1755 y}{2} - \frac{585}{2} + - 22 y = 64

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

\displaystyle - \frac{1799 y}{2} = 356.5

Now we divide by \displaystyle - \frac{1799}{2}.

\displaystyle y = -0.39633129516398

Now round to the nearest hundredth.

\displaystyle y= -0.4

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

\displaystyle 2 x + -17.8349082823791 = -15

\displaystyle 2 x - 17.8349082823791 = -15

Now we add -17.8349082823791 to each side.

\displaystyle 2 x = 2.8349082823791

Now we divide by \displaystyle 2

\displaystyle x = 1.41745414118955

 

Now round to the nearest hundredth.

\displaystyle x= 1.42

Example Question #69 : Reasoning With Equations & Inequalities

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

\displaystyle - 32 x + 22 y = 61

\displaystyle 39 x - 34 y = 53

Possible Answers:

\displaystyle x = -14.09 , y = -17.72

\displaystyle x = -9.34 , y = 18.4

\displaystyle x = 12.66 , y = 5.59

\displaystyle x = -12.55 , y = 5.44

\displaystyle x = -6.05 , y = -2.64

Correct answer:

\displaystyle x = -14.09 , y = -17.72

Explanation:

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

\displaystyle - 32 x + 22 y = 61

Now we subtract \displaystyle 22 y from each side.

\displaystyle - 32 x + 22 y - 22 y = 61 - 22 y

Now we divide by \displaystyle -32

\displaystyle x = \frac{11 y}{16} - \frac{61}{32}

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

\displaystyle 39 x - 34 y = 53

\displaystyle \frac{429 y}{16} - \frac{2379}{32} + - 34 y = 53

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

\displaystyle - \frac{115 y}{16} = 127.34375

Now we divide by \displaystyle - \frac{115}{16} .

\displaystyle y = -17.7173913043478

Now round to the nearest hundredth.

\displaystyle y= -17.72

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

\displaystyle - 32 x + -389.78260869565213 = 61

\displaystyle - 32 x - 389.782608695652 = 61

Now we add \displaystyle 389.78260869565213 to each side.

\displaystyle - 32 x = 450.78260869565213

Now we divide by \displaystyle -32

\displaystyle x = -14.0869565217391

 

Now round to the nearest hundredth.

\displaystyle x= -14.09

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

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

\displaystyle 49 x + 10 y = -64

\displaystyle 8 x + 30 y = 3

Possible Answers:

\displaystyle x = -7.24 , y = -8.12

\displaystyle x = 17.58 , y = 14.32

\displaystyle x = -8.46 , y = -10.92

\displaystyle x = -1.4 , y = 0.47

\displaystyle x = -10.89 , y = 19.98

Correct answer:

\displaystyle x = -1.4 , y = 0.47

Explanation:

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

\displaystyle 49 x + 10 y = -64

Now we subtract \displaystyle 10 y from each side.

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

Now we divide by \displaystyle 49

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

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

\displaystyle 8 x + 30 y = 3

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

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

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

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

\displaystyle y = 0.47410071942446

Now round to the nearest hundredth.

\displaystyle y= 0.47

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

\displaystyle 49 x + 4.741007194244603 = -64

Now we subtract \displaystyle 4.741007194244603 from each side.

\displaystyle 49 x = -68.7410071942446

Now we divide by \displaystyle 49

\displaystyle x = -1.40287769784173

 

Now round to the nearest hundredth.

\displaystyle x= -1.4

Example Question #2 : Solve System Of Equations Using Substitution: Ccss.Math.Content.Hsa Rei.C.5

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

\displaystyle 31 x + 29 y = -83

\displaystyle - 43 x - 12 y = 8

Possible Answers:

\displaystyle x = -2.04 , y = 8.04

\displaystyle x = -11.77 , y = -10.06

\displaystyle x = 0.87 , y = -3.8

\displaystyle x = -18.9 , y = 17.82

\displaystyle x = 17.06 , y = 3.32

Correct answer:

\displaystyle x = 0.87 , y = -3.8

Explanation:

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

\displaystyle 31 x + 29 y = -83

Now we subtract \displaystyle 29 y from each side.

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

Now we divide by \displaystyle 31

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

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

\displaystyle - 43 x - 12 y = 8

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

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

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

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

\displaystyle y = -3.79542857142857

Now round to the nearest hundredth.

\displaystyle y= -3.8

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

\displaystyle 31 x + -110.06742857142856 = -83

\displaystyle 31 x - 110.067428571429 = -83

Now we add \displaystyle 110.06742857142856 to each side.

\displaystyle 31 x = 27.067428571428565

Now we divide by \displaystyle 31

\displaystyle x = 0.873142857142857

 

Now round to the nearest hundredth.

\displaystyle x= 0.87

 

Example Question #3 : Solve System Of Equations Using Substitution: Ccss.Math.Content.Hsa Rei.C.5

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

\displaystyle - 6 x + 10 y = 80

\displaystyle - 39 x + 13 y = -99

Possible Answers:

\displaystyle x = -3.06 , y = -14.65

\displaystyle x = 5.22 , y = -13.66

\displaystyle x = -7.59 , y = -8.95

\displaystyle x = -15.46 , y = 6.84

\displaystyle x = 6.51 , y = 11.9

Correct answer:

\displaystyle x = 6.51 , y = 11.9

Explanation:

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

\displaystyle - 6 x + 10 y = 80

Now we subtract \displaystyle 10 y from each side.

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

Now we divide by \displaystyle -6

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

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

\displaystyle - 39 x + 13 y = -99

\displaystyle - 65 y + 520 + 13 y = -99

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

\displaystyle - 52 y = -619.0

Now we divide by \displaystyle -52.

\displaystyle y = 11.9038461538462

Now round to the nearest hundredth.

\displaystyle y= 11.9

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

\displaystyle - 6 x + 119.03846153846153 = 80

Now we subtract \displaystyle 119.03846153846153 from each side.

\displaystyle - 6 x = -39.03846153846153

Now we divide by \displaystyle -6

\displaystyle x = 6.50641025641026

 

Now round to the nearest hundredth.

\displaystyle x= 6.51

 

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