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Which statements are true about the ordered pair (10, 5) and the system of equations?
(Look at the file to answer the question)

Which Statements Are True About The Ordered Pair 10 5 And The System Of Equations Look At The File To Answer The Question class=

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Answers:

The first and third options should be selected.

  • The ordered pair (10,5) is a solution to the first equation because it makes the first equation true.
  • The ordered pair (10,5) is not a solution to the system because it makes at least one of the equations false.

Explanation:

In order for a point to be a solution to a system of equations, it must make both equations true when its x and y values are substituted in. That being said, we need to test if (10,5) is a solution for the two equations.

Let's try the first equation. Substitute 10 for x and 5 for y and solve:

[tex]2x - 5y = -5\\2(10) - 5(5) = -5\\20 - 25 = -5\\-5 = -5[/tex]

-5 does equal -5, so (10,5) is a solution to the first equation.

Next, let's test the second equation. Do the same:

[tex]x + 2y = 11\\(10) + 2 (5) = 11\\10 + 10 = 11\\20 = 11[/tex]

However, 20 does not equal 11, therefore (10,5) is not a solution to the second equation.

So far, we know that (10,5) is a solution to the first equation, but not the second equation. Knowing this, it cannot  be a solution to the system because it does not make both equations true. Therefore, only the first and third options should be selected.

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