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olga_2 [115]
3 years ago
6

Systems of Linear Equations What are the different ways to solve a system of linear equations? When do you get an answer to a sy

stem of linear equations that has one solution, no solution and infinitely many solutions? Solve each of the following systems by graphing. y = -x – 7 y = 4/3 x – 7 y = -3x – 5 y = x + 3 y = -2x + 5 y = 1/3 x – 2 3x + 2y = 2 x + 2y = -2 x + 3y = -9 2x – y = -4 x – 2y = 2 -x + 4y = -8 5x + y = -2 x + y = 2

Mathematics
2 answers:
Mrac [35]3 years ago
3 0

Answer:

Different ways to solve a system of linear equations:

  • isolate one variable in one equation and replace it in the other equation
  • multiply/divide one equation by a constant and then add/subtract it to the other one, so that only one variable remains
  • graph the equation and look at the intersection point

If you graph the system:

  • there is only one solution if the lines intersects at only one point
  • there is no solution if the lines don't intersect each other (they are parallel)
  • there are infinitely many solutions if the lines overlap each other (they are the same equation multiplied by some constant)

Step-by-step explanation:

1st system

y = -x – 7  

y = 4/3 x – 7  

solution: x= 0, y = 7

2nd system

y = -3x – 5  

y = x + 3  

solution: x = -2, y = 1

3rd system

y = -2x + 5  

y = 1/3 x – 2

solution:  x = 3, y = -1

4th system

3x + 2y = 2  

x + 2y = -2  

solution: x = 2, y = -2

5th system

x + 3y = -9  

2x – y = -4

solution:  x = -3, y = -2

6th system

x – 2y = 2

-x + 4y = -8

solution:  x = -4, y = -3

7th system

5x + y = -2  

x + y = 2

solution: x = -1, y = -3

nignag [31]3 years ago
3 0

75% I think x = -1, y = -3

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guajiro [1.7K]

the graph of 13y + kx = 4 and the line containing the points (5, -8) and (2, 4) are parallel.

We find the slope of parallel line using two given points

(5, -8) and (2, 4)

Slope formula is

slope = \frac{y_2-y_1}{x_2-x_1}

slope = \frac{4-(-8)}{2-5}

slope = \frac{12)}{-3}=-4

so slope = -4

Slope of any two parallel lines are always equal

Lets find the slope of the equation 13y + kx = 4

Subtract kx on both sides

13 y = -kx + 4

Divide both sides by 13

y= \frac{-kx}{13} + \frac{4}{13}

Now slope = -k/13

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So the slope of 13y + kx = 4  is also -4

Hence we equation the slope and find out k

\frac{-k}{13}=-4

Multiply by 13 on both sides and divide by -1

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the value of k = 52

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3 years ago
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Answer:

a

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b

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Step-by-step explanation:

From the question we are told that

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Given that the confidence level is  95% then the level of significance is mathematically represented as

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=>         \alpha  =  5\%

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Generally the margin of error is mathematically represented as

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=>     E =  1.96 *  \frac{108}{\sqrt{453} }

=>      E = 9.946

Generally the 95% confidence interval is mathematically represented as

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=>         1013  - 9.946  <  \mu < 1013  + 9.946

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