The number of counties in state a and the number of counties in state b are consecutive even integers whose sum is 162. if state a has more counties than state b, how many counties does each state have?

The number of counties in state A is 82 and the number of counties in state B is 80

Step-by-step explanation:

Let

x -----> the number of counties in state B

x+2 -----> the number of counties in state A

we know that

The sum of counties in state A and state B must be equal to 162

Solve for x

Group terms that contain the same variable and move the constant to the other side

Combine like terms

Divide by 2 both sides

so

therefore

The number of counties in state A is 82 and the number of counties in state B is 80

22

step-by-step explanation:

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,