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These are only three of the infintely many solutions to this equation.

Sample set a

Find a solution to each of the following linear equations in two variables and write the solution as an ordered pair.

y = 3 x 6 , if x = 1

Substitute 1 for x , compute, and solve for y .

y = 3 ( 1 ) 6 = 3 6 = 3

Hence, one solution is ( 1 , 3 ) .

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y = 15 4 x , if x = 10

Substitute 10 for x , compute, and solve for y .

y = 15 4 ( 10 ) = 15 + 40 = 55

Hence, one solution is ( 10 , 55 ) .

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b = 9 a + 21 , if a = 2

Substitute 2 for a , compute, and solve for b .

b = 9 ( 2 ) + 21 = 18 + 21 = 3

Hence, one solution is ( 2 , 3 ) .

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5 x 2 y = 1 , if x = 0

Substitute 0 for x , compute, and solve for y .

5 ( 0 ) 2 y = 1 0 2 y = 1 2 y = 1 y = 1 2

Hence, one solution is ( 0 , 1 2 ) .

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Practice set a

Find a solution to each of the following linear equations in two variables and write the solution as an ordered pair.

y = 7 x 20 , if x = 3

( 3 , 1 )

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m = 6 n + 1 , if n = 2

( 2 , 11 )

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b = 3 a 7 , if a = 0

( 0 , 7 )

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10 x 5 y 20 = 0 , if x = 8

( 8 , 20 )

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3 a + 2 b + 6 = 0 , if a = 1

( 1 , 3 2 )

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Exercises

For the following problems, solve the linear equations in two variables.

y = 8 x + 14 , if x = 1

( 1 , 22 )

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y = 2 x + 1 , if x = 0

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y = 5 x + 6 , if x = 4

( 4 , 26 )

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x + y = 7 , if x = 8

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3 x + 4 y = 0 , if x = 3

( 3 , 9 4 )

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2 x + y = 1 , if x = 1 2

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5 x 3 y + 1 = 0 , if x = 6

( 6 , 29 3 )

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4 x 4 y = 4 , if y = 7

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2 x + 6 y = 1 , if y = 0

( 1 2 , 0 )

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x y = 0 , if y = 14 3

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y = x , if x = 1

( 1 , 1 )

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x + y = 0 , if x = 0

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y + 3 4 = x , if x = 9 4

( 9 4 , 3 2 )

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y + 17 = x , if x = 12

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20 y + 14 x = 1 , if x = 8

( 8 , 111 20 )

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3 5 y + 1 4 x = 1 2 , if x = 3

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1 5 x + y = 9 , if y = 1

( 40 , 1 )

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y + 7 x = 0 , if x = A star

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2 x + 31 y 3 = 0 , if x = a

( a , 3 2 a 31 )

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436 x + 189 y = 881 , if x = 4231

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y = 6 ( x 7 ) , if x = 2

( 2 , 30 )

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y = 2 ( 4 x + 5 ) , if x = 1

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5 y = 9 ( x 3 ) , if x = 2

( 2 , 9 5 )

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3 y = 4 ( 4 x + 1 ) , if x = 3

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2 y = 3 ( 2 x 5 ) , if x = 6

( 6 , 21 2 )

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8 y = 7 ( 8 x + 2 ) , if x = 0

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b = 4 a 12 , if a = 7

( 7 , 40 )

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b = 5 a + 21 , if a = 9

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4 b 6 = 2 a + 1 , if a = 0

( 0 , 7 4 )

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5 m + 11 = n + 1 , if n = 4

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3 ( t + 2 ) = 4 ( s 9 ) , if s = 1

( 1 , 38 3 )

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7 ( t 6 ) = 10 ( 2 s ) , if s = 5

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y = 0 x + 5 , if x = 1

( 1 , 5 )

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2 y = 0 x 11 , if x = 7

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y = 0 x + 10 , if x = 3

( 3 , 10 )

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5 y = 0 x 1 , if x = 0

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y = 0 ( x 1 ) + 6 , if x = 1

( 1 , 6 )

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y = 0 ( 3 x + 9 ) 1 , if x = 12

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Calculator problems

An examination of the winning speeds in the Indianapolis 500 automobile race from 1961 to 1970 produces the equation y = 1.93 x + 137.60 , where x is the number of years from 1960 and y is the winning speed. Statistical methods were used to obtain the equation, and, for a given year, the equation gives only the approximate winning speed. Use the equation y = 1.93 x + 137.60 to find the approximate winning speed in

  1. 1965
  2. 1970
  3. 1986
  4. 1990

(a) Approximately 147 mph using ( 5 , 147.25 )
(b) Approximately 157 mph using ( 10 , 156.9 )
(c) Approximately 188 mph using ( 26 , 187.78 )
(d) Approximately 196 mph using ( 30 , 195.5 )

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In electricity theory, Ohm’s law relates electrical current to voltage by the equation y = 0.00082 x , where x is the voltage in volts and y is the current in amperes. This equation was found by statistical methods and for a given voltage yields only an approximate value for the current. Use the equation y = 0.00082 x to find the approximate current for a voltage of

  1. 6 volts
  2. 10 volts

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Statistical methods have been used to obtain a relationship between the actual and reported number of German submarines sunk each month by the U.S. Navy in World War II. The equation expressing the approximate number of actual sinkings, y , for a given number of reported sinkings, x , is y = 1.04 x + 0.76 . Find the approximate number of actual sinkings of German submarines if the reported number of sinkings is

  1. 4
  2. 9
  3. 10

(a) Approximately 5 sinkings using ( 4 , 4.92 )
(b) Approximately 10 sinkings using ( 9 , 10.12 )
(c) Approximately 11 sinkings using ( 10 , 11.16 )

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Statistical methods have been used to obtain a relationship between the heart weight (in milligrams) and the body weight (in milligrams) of 10-month-old diabetic offspring of crossbred male mice. The equation expressing the approximate body weight for a given heart weight is y = 0.213 x - 4.44 . Find the approximate body weight for a heart weight of

  1. 210 mg
  2. 245 mg

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Statistical methods have been used to produce the equation y = 0.176 x 0.64 . This equation gives the approximate red blood cell count (in millions) of a dog’s blood, y , for a given packed cell volume (in millimeters), x . Find the approximate red blood cell count for a packed cell volume of

  1. 40 mm
  2. 42 mm

(a) Approximately 6.4 using ( 40 , 6.4 )
(b) Approximately 4.752 using ( 42 , 7.752 )

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An industrial machine can run at different speeds. The machine also produces defective items, and the number of defective items it produces appears to be related to the speed at which the machine is running. Statistical methods found that the equation y = 0.73 x 0.86 is able to give the approximate number of defective items, y , for a given machine speed, x . Use this equation to find the approximate number of defective items for a machine speed of

  1. 9
  2. 12

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A computer company has found, using statistical techniques, that there is a relationship between the aptitude test scores of assembly line workers and their productivity. Using data accumulated over a period of time, the equation y = 0.89 x 41.78 was derived. The x represents an aptitude test score and y the approximate corresponding number of items assembled per hour. Estimate the number of items produced by a worker with an aptitude score of

  1. 80
  2. 95

(a) Approximately 29 items using ( 80 , 29.42 )
(b) Approximately 43 items using ( 95 , 42.77 )

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Chemists, making use of statistical techniques, have been able to express the approximate weight of potassium bromide, W , that will dissolve in 100 grams of water at T degrees centigrade. The equation expressing this relationship is W = 0.52 T + 54.2 . Use this equation to predict the potassium bromide weight that will dissolve in 100 grams of water that is heated to a temperature of

  1. 70 degrees centigrade
  2. 95 degrees centigrade

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The marketing department at a large company has been able to express the relationship between the demand for a product and its price by using statistical techniques. The department found, by analyzing studies done in six different market areas, that the equation giving the approximate demand for a product (in thousands of units) for a particular price (in cents) is y = 14.15 x + 257.11 . Find the approximate number of units demanded when the price is

  1. $ 0.12
  2. $ 0.15

(a) Approximately 87 units using ( 12 , 87.31 )
(b) Approximately 45 units using ( 15 , 44.86 )

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The management of a speed-reading program claims that the approximate speed gain (in words per minute), G , is related to the number of weeks spent in its program, W , is given by the equation G = 26.68 W 7.44 . Predict the approximate speed gain for a student who has spent

  1. 3 weeks in the program
  2. 10 weeks in the program

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Exercises for review

( [link] ) Find the product. ( 4 x 1 ) ( 3 x + 5 ) .

12 x 2 + 17 x 5

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( [link] ) Find the product. ( 5 x + 2 ) ( 5 x 2 ) .

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( [link] ) Solve the equation 6 [ 2 ( x 4 ) + 1 ] = 3 [ 2 ( x 7 ) ] .

x = 0

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( [link] ) Solve the inequality 3 a ( a 5 ) a + 10 .

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( [link] ) Solve the compound inequality 1 < 4 y + 11 < 27 .

3 < y < 4

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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
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what is physics
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A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
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Can you compute that for me. Ty
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what is the dimension formula of energy?
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what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
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2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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