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Determine the number of solutions for this system of equations by inspection only. Explain.
5x+4y=13
35x+28y=104
Select the correct answer below and fill in the answer box to complete your choice.

A. There is one solution if the first equation is multiplied by _, the X-terms will be the same but the y-terms will not. So, the x-term will be eliminated leaving a y-term and a constant.

B. There are infinitely many solutions. if the first equation is multiplied by_, the like variable terms and Constants will be the same so each term will be eliminated this result in the statement 0=0 which is true.

C. There is no solution if the first equation is multiplied by_, the like variable terms will have the same coefficients but the contestants will not be the same so the variable terms will be eliminated but the constant term will not be zero this results in a statement that is not true​

Respuesta :

facundo3141592

The system of equations has no solutions because the lines are parallel, so the correct option is C.

How many solutions does a linear system have?

Here we have the system of equations:

5*x + 4*y = 13

35*x + 28*y = 104

Something that you can notice, is that:

  • 35 is 7 times 5.
  • 28 is 7 times 4.

Then if we divide the second equation by 7 we get:

(35*x + 28*y)/7 = 104/7

5*x + 4*y = 14.86

Then our system of equations is:

5*x + 4*y = 13

5*x + 4*y = 14.86

As you can see, the left side is the same in both equations, but the right side (the constant part) is not.

This means that the lines are parallel, thus their graphs never intersect, so the system of equations has no solution.

Then the correct option is C. (in this method you need to multiply the first equation by 7, instead of dividing the second by 7, these are equivalent steps)

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

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