Question

Vineet solved a system of equations by substitution. In his work, he substituted an expression for one of the variables and solved for the value of the other. This resulted in the equation 7=9. What can Vineet conclude?

A) The solution to the system is (7,9).
B) The system of linear equations does not have a solution.
C) The work must be incorrect because it is not possible to get this equation.
D) The system of equations has infinitely many solutions.

Answer 1

The equation 7=9 is an inconsistency indicating that the system of equations solved by substitution has no solution, which means option B is the correct answer.

Step-by-step explanation:

When Vineet solved a system of equations by substitution and the result was the equation 7=9, it demonstrates an inconsistency. Such an equation suggests that there is no set of values for the variables that makes both original equations true simultaneously, hence the system of equations has no solution. This is directly related to the concept of linear equations where a system can either have one solution, no solution, or infinitely many solutions. In this scenario, the correct conclusion Vineet can make is option B: The system of linear equations does not have a solution. The false mathematical statement 7=9 is a clear indication of an inconsistent system.