Final answer:
To ensure that the system of equations is consistent, b2 must be equal to 2.
Step-by-step explanation:
To ensure that the given system of equations is consistent, the coefficients of the variables must satisfy a certain relation. Let's consider the system of equations:
361b1 + 7b2 + 5b3 = 0
5b1 + 4b2 + bg = 0
To determine the relation, we need to apply the junction rule and obtain a single equation. Since we have one unknown, we only need one equation. By subtracting 5b1 from both sides of the second equation, we get:
5b2 + 4b2 + bg - 5b1 = 0
Now, the coefficients of b1, b2, and b3 must satisfy the relation: 361 - 5 = 7 - 4 = 5 - 0. This means that b1 and b3 can have any values, but b2 must be equal to 2. Therefore, the relation that must be satisfied is b2 = 2.