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.
