Determine whether the following statement is true or false I

Determine whether the following statement is true or false. If false, say why. The following system has the solution set Phi. x + y = 10 x + y = 9 Choose the correct answer below True, because the system is consistent and the equations are independent False, because the system is consistent and the equations are dependent True, because the system is inconsistent and the equations are independent.

Solution

x+y = 10

x+y = 9

In order to explain the correct option, we need to solve the system of equations

Subtracting equation (2) from equation (1)

x+y = 10     => x+y = 10

-(x+y = 9)    => -x -y = -9

                     ---------------------

                             0 = 1

0 can never be equal to 1. Therefore the solutions set would be fi (an empty set or no solutions) and system is inconsistent.

So, option C) is correct.