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Determine what kind of solution you would expect from the system of equations 3x - 8y = 10 and 16x - 32y = 75 without graphing the system. Explain how you determined your answer.

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MathPhys

Step-by-step explanation:

If two lines have the same slope and the same y-intercept, there are infinite solutions.

If two lines have the same slope and different y-intercepts, there are zero solutions.

Otherwise, if the two lines have different slopes, then there is one solution.

The slope of the first line is 3/8.  The slope of the second line is 16/32 = 1/2.  The slopes are different, so there is only one solution.

The solution of the given system of equations is (x, y) = (8.75, 2).

What is a Linear equation of two variables?

  • These are the system of equations with two variables having a no solution, unique solution or infinitely many solutions.
  • The highest order of the equation for this systems is one.

Given: System of equations

3x - 8y = 10                           …(1)

16x - 32y = 75                       …(2)

Consider equation (2).

⇒ 16x - 32y = 75

Dividing both sides by 16, we get:

⇒ x - 2y = 75/16

⇒ x = 2y + 75/16                  …(3)

Now, substitute the value of x = 2y + 75/16 in equation (1), we get:

⇒ 3(2y + 75/16) - 8y = 10

⇒ 6y + 225/16 - 8y = 10

⇒ 2y = 225/16 - 10

⇒ 2y = (225 - 160)/16

⇒ 2y = 65/16

⇒ y = 65/32

⇒ y ≈ 2

Now, put the value of y = 65/32 in equation (3), we get:

⇒ x = 2(65/32) + 75/16

⇒ x = (65/16) + (75/16)

⇒ x = 140/16

⇒ x = 8.75

Therefore, the solution for the given simultaneous equation is;

(x, y) = (8.75, 2)

Learn more about the Linear equations of two variables here: https://brainly.com/question/13052704?referrer=searchResults

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