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?

Question

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

Answer 1

If Vineet arrived at the equation \(7 = 9\) while solving the system of equations, this is a contradiction, as \(7\) is not equal to \(9\). When a contradiction like this occurs, it implies that there is no solution to the system of equations. Therefore, Vineet can conclude that:

The system of equations does not have a solution.