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Jet001 [13]
3 years ago
9

selesaikan sistem persamaan linear dua variabel berikut dengan menggunakan metode subtitusi 5x+3y= 16 dan x+3y=8

Mathematics
2 answers:
Andreyy893 years ago
7 0

The solution set for the system of linear equations 5x + 3y = 16 and x + 3y = 8is\boxed{\left\{ {\left( {{\mathbf{2,2}}} \right)} \right\}}.

Further explanation:

It is given that the system of linear equations are 5x + 3y = 16andx + 3y = 8.

Consider the given equations as follows:

\begin{aligned}5x+3y=16\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,......\left(1\right)\hfill\\x+3y=8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,......\left(2\right)\hfill\\\end{aligned}

Isolate the variable y in terms of x from equation (1) as follows:

\begin{aligned}5x+3y&=16\\3y&=16-5x\\y&=\frac{{16-5x}}{3}\\\end{aligned}

Therefore, the value of y in terms of x is\frac{{16-5x}}{3}.

Now, substitute \frac{{16-5x}}{3} for y in the equation (2) as follows:

x+3\left({\frac{{16-5x}}{3}}\right)=8

The variable is eliminated in the above equation.

Simplify the equation as follows:

\begin{aligned}x+3\left({\frac{{16-5x}}{3}}\right)&=8\\x+16-5x&=8\\-4x+16&=8\\-4x&=8-16\\\end{aligned}

Further simplify theequation.

\begin{aligned}-4x&=-8\\x&=\frac{8}{4}\\x&=2\\\end{aligned}

Therefore, the value of xis {\mathbf{2}}.

Substitute 2 for x in the equation (1) and obtain the value of y as shown below.

\begin{aligned}5\left(2\right)+3y&=16\\10+3y&=16\\3y&=16-10\\3y&=6\\\end{aligned}

Further simplify the above equation.

\begin{aligned}y&=\frac{6}{3}\\&=2\\\end{aligned}

Therefore, the value of yis {\mathbf{2}}.

Thus, the ordered pair for the system of linear equation is \left( {{\mathbf{2,2}}} \right).

Check whether the obtained solution \left( {2,2} \right) satisfies the given equations or not.

Substitute 2 for x and 2 for y in the equation (1) and check the equation.

\begin{aligned}5\left(2\right)+3\left(2\right)\mathop&=\limits^?16\hfill\\\,\,\,\,\,\,\,\,\,\,\,\,10+6\mathop&=\limits^?16\hfill\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,16&=16\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {{\text{True}}}\right)\hfill\\\end{aligned}

The ordered pair \left( {2,2} \right) satisfies the equation (1).

Substitute 2 for x and 2 for y in the equation (2) and check the equation.

\begin{aligned}2+3\left(2\right)\mathop&=\limits^?8\hfill\\\,\,\,\,\,\,\,2+6\mathop&=\limits^? 8\hfill\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,8&=8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left({{\text{True}}}\right)\hfill\\\end{aligned}

The ordered pair \left( {2,2} \right) satisfies the equation (2).

Thus, the solution set for the system of linear equations 5x + 3y = 16 and x + 3y = 8is\boxed{\left\{ {\left( {{\mathbf{2,2}}} \right)} \right\}}.

Learn more:

1. Which classification best describes the following system of equations? brainly.com/question/9045597

2. Which polynomial is prime?brainly.com/question/1441585

3. Write the subtraction fact two ways 10-3? brainly.com/question/6208262

Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Linear equations

Keywords:Substitution, linear equation, system of linear equations in two variables, variables, mathematics,5x + 3y = 16,x + 3y = 8

mote1985 [20]3 years ago
3 0
3x – 7y=16<span> ... Grafik dari persamaan </span>linear dua variabel<span>berbentuk garis luru
s, seperti yang ... SPLDV dengan </span>metode substitusi<span>, perhatikan contoh </span>berikut<span>. .... Jadi solusi </span>sistem persamaan<span> linier di atas adalah </span>x<span> = 2, y = </span>3<span>, z = 4. .... </span>8<span>. Berapakah nilai 6 − 2 jika </span><span>  merupakan penyelesaian dari ...</span>
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Answer:

126

Step-by-step explanation:

Total volume of sand = pi/3*(6^2)*(15) + pi*(6)^2*(30) = 1260*pi mm^3

So it will therefore take 1260*pi/10*pi = 126 seconds for all of the sand from the top hourglass to drip down to the bottom hourglass.

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3 years ago
The drama club was selling tickets
Lubov Fominskaja [6]

Answer:

108 student tickets, and 176 adult tickets  were sold

Step-by-step explanation:

Adult ticket $8  Call the number of adult tickets sold "a"

Student ticket $5  Call the number of student tickets sold "s"

Since we are talking about TWO consecutive days of sold out seats, the total number of seats sold were 2* 142 = 284

Then we create two different equations with the information given:

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8 a + 5 (284 - a) = 1948

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a = 528/3

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5 0
2 years ago
Evaluate 3 to the 2nd power + (6 - 2) x 4- 6 over 3
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Answer:

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Step-by-step explanation:

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then multiply by 4

4x4 is 16

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4 0
3 years ago
A blackjack player at a Las Vegas casino learned that the house will provide a free room if play is for four hours at an average
marysya [2.9K]

Answer:

a) player’s expected payoff is $ 240

b) probability the player loses $1000 or more is 0.1788

c)  probability the player wins is 0.3557

d) probability of going broke is 0.0594

Step-by-step explanation:

Given:

Since there are 60 hands per hour and the player plays for four hours then the sample size is:

n = 60 * 4 = 240

The player’s strategy provides a probability of .49 of winning on any one hand so the probability of success is:

p = 0.49

a)

Solution:

Expected payoff is basically the expected mean

Since the bet is $50 so $50 is gained when the player wins a hand and $50 is lost when the player loses a hand. So

Expected loss =  μ

                        = ∑ x P(x)

                        = 50 * P(win) - 50 * P(lose)

                        = 50 * P(win) + (-50) * (1 - P(win))

                         = 50 * 0.49 - 50 * (1 - 0.49)

                        = 24.5 - 50 ( 0.51 )

                        = 24.5 - 25.5

                        = -1

Since n=240 and expected loss is $1 per hand then the expected loss in four hours is:

240 * 1 = $ 240

b)

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 110.5 - 117.6 / √117.6(1-0.49)

  = −7.1/√117.6(0.51)

  = −7.1/√59.976

  = −7.1/7.744417

  =−0.916789

Here the player loses 1000 or more when he loses at least 130 of 240 hands so the wins is 240-130 = 110

Using normal probability table:

P(X≤110) = P(X<110.5)

             = P(Z<-0.916)

             = 0.1788

c)

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 120.5 - 117.6 / √117.6(1-0.49)

  = 2.9/√117.6(0.51)

  = 2.9/√59.976

  = 2.9/7.744417

  =0.374463

Here the player wins when he wins at least 120 of 240 hands

Using normal probability table:

P(X>120) = P(X>120.5)

              = P(Z>0.3744)  

             =  1 - P(Z<0.3744)

             = 1 - 0.6443

             = 0.3557

d)

Player goes broke when he loses $1500

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 105.5 - 117.6 / √117.6(1-0.49)

  = -12.1/√117.6(0.51)

  = -12.1/√59.976

  = -12.1/7.744417

  =−1.562416

Here the player loses 1500 or more when he loses at least 135 of 240 hands so the wins is 240-135 = 105

Using normal probability table:

P(X≤105) = P(X<105.5)

             = P(Z<-1.562)

             = 0.0594

7 0
3 years ago
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