Final answer:
To create an inconsistent system with the equation x - 2y = 5, the equation 6x + 12y = 30 can be used. However, solving the system of equations shows that they are consistent.
Step-by-step explanation:
To create an inconsistent system with the equation x - 2y = 5, we need to find another equation that cannot be satisfied at the same time. Looking at the options given, the equation 6x + 12y = 30 creates an inconsistent system. Let's solve the system of equations to verify:
Equation 1: x - 2y = 5
Equation 2: 6x + 12y = 30
We can solve Equation 1 for x: x = 5 + 2y
Substituting this value into Equation 2: 6(5 + 2y) + 12y = 30
Expanding and simplifying: 30 + 12y + 12y = 30
Combining like terms: 24y + 30 = 30
Subtracting 30 from both sides: 24y = 0
Dividing by 24: y = 0
Substituting this value into Equation 1: x = 5 + 2(0) = 5
The system has a solution of x = 5 and y = 0, which means the two equations are consistent. Therefore, the equation 6x + 12y = 30 does not pair with x - 2y = 5 to create an inconsistent system.