Why is (6, –2) not a solution to the system of equations given below? a. it satisfies the top equation but not the bottom equation. b. it satisfies the bottom equation but not the top equation. c. it doesn’t satisfy either the top or the bottom equations. d. it satisfies both the top and the bottom equations.

The system of equations is not given, therefore, I can only help with the concept.

For an order pair to be referred to as a solution to the system, this order pair MUST SATISFY BOTH equations.

This means that, if:
1- The order pair doesn't satisfy one of the equations, or
2- Doesn't satisfy both equations, then
It will not be referred to as a solution

Based on the above, all you have to do is substitute with the given pair in the two equations. If the two equations are satisfied, then it is a solution. Otherwise, it is not.

Let's look at some examples to show the three cases mentioned above:
1- Assume that the two equations are:
y = x - 8
x + y = 4
The order pair given is (6 ,-2)
Substitute in the first equation:
y = 6 - 8 = -2 > equation is satisfied
Substitute in second equation:
6 + (-2) = 6 - 2 = 4 > equation is satisfied
Since the order pair satisfies both equations, then it is a solution to the system

2- Assume that the system of equations is:
y = 2x
y = x - 9
The order pair given is (6,-2)
Substitute in the first equation:
y = 2(6) = 12 ≠ -2 > equation is not satisfied
Substitute in the second equation:
y = 6 - 9 = -3 ≠ -2 > equation is not satisfied
Since neither of the equations is satisfied, therefore (6,-2) is not a solution to this system

3- Assume that the system of equations is:
y = 2x - 14
y = -4x
The given order pair is (6,-2)
Substitute in the first equation:
y = 2(6) - 14 = 12 - 14 = -2 > equation is satisfied
Substitute in the second equation:
y = -4(6) = -24 ≠ -2 > equation is not satisfied
Since only one of the equations is satisfied, therefore, the given order pair is not a solution for this system

Hope this helps :)