The question is asking us to decide if the ordered pair (4,2) is a solution to the following system of equations:
1) -10x - 4y = -52
2) -x - 4y = -16
We have an ordered pair (4, 2), where the first number refers to the x-coordinate and the second number to the y-coordinate.
For this problem, we will substitute these coordinates (x=4, y=2) into each of our system equations to determine if they are true statements.
Let's start with the first equation:
Substitute x=4, y=2 into -10x - 4y = -52:
When we do that we get -40 - 8, which equals -48. So, this does not satisfy the equation -10x - 4y = -52 because -48 is not equal to -52. Therefore, the ordered pair is not a solution for the first equation.
Let's try to see with the second equation:
Substitute x=4, y=2 into -x - 4y = -16:
When we substitute in those values we will get -4 - 8 = -12. This does not satisfy the equation -x - 4y = -16 because -12 is not equal to -16. Therefore, the ordered pair is not a solution for the second equation as well.
In conclusion, the ordered pair (4,2) is not a solution to the system of equations because it does not satisfy both equations.