Answer: The solution to a system of equations in two variables represents the values of the variables that satisfy both equations simultaneously.
To check which equations might make up the system with a solution of (5,-19), we can substitute x = 5 and y = -19 into each equation and see if they are both satisfied.
Substituting x = 5 and y = -19 into the first equation, we get:
y = 2x - 23
-19 = 2(5) - 23
-19 = -13
This is not true, so the first equation is not part of the system.
Substituting x = 5 and y = -19 into the second equation, we get:
y = x - 17
-19 = 5 - 17
-19 = -12
This is not true, so the second equation is not part of the system.
Substituting x = 5 and y = -19 into the third equation, we get:
y = -7x + 16
-19 = -7(5) + 16
-19 = -19
This is true, so the third equation is one of the equations in the system.
Substituting x = 5 and y = -19 into the fourth equation, we get:
y = -21 - 9x
-19 = -21 - 9(5)
-19 = -64
This is not true, so the fourth equation is not part of the system.
Substituting x = 5 and y = -19 into the fifth equation, we get:
y = -3x - 6
-19 = -3(5) - 6
-19 = -21
This is not true, so the fifth equation is not part of the system.
Therefore, one possible system of equations with a solution of (5,-19) is:
y = -7x + 16
We would need another equation to form a complete system with a unique solution.
Explanation: