Question

Which statements are true about the ordered pair (10, 5) and the system of equations? 2x-5y=-5x 2y=11? Select each correct answer.

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

Answer 1

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

Step-by-step explanation:

In order to determine which statements are true about the ordered pair (10, 5) and the system of equations 2x-5y=-5x and 2y=11, we need to substitute the values of x and y from the ordered pair into each equation and see if the equation is true.

1. The first equation becomes: 2(10) - 5(5) = -5(10). Simplifying, we get 20 - 25 = -50, which is false. Therefore, the ordered pair (10, 5) is not a solution to the first equation. So, statement 1 is false.
2. The second equation becomes: 2(5) = 11. Simplifying, we get 10 = 11, which is false. Therefore, the ordered pair (10, 5) is not a solution to the second equation. So, statement 2 is false.
3. Since both equations are false when we substitute the values of x and y from the ordered pair (10, 5), the ordered pair (10, 5) is not a solution to the system of equations. So, statement 3 is true.
4. Since both equations are false when we substitute the values of x and y from the ordered pair (10, 5), the ordered pair (10, 5) is not a solution to the system of equations. So, statement 4 is false.

In conclusion, the true statements about the ordered pair (10, 5) and the system of equations are: statement 3 is true.