Question

interpreting work when solving systems 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? 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.

Explanation:

When solving a system of equations, if substitution leads to a false numerical statement (like $7=9$, which is never true), this means the lines represented by the equations are parallel and never intersect. Such systems have no solution. It is possible to get this result with correct substitution for inconsistent systems, so the work is not necessarily wrong. A solution $(7,9)$ would require satisfying both original equations, and infinitely many solutions come from a true identity like $5=5$, not a false statement.

Answer:

The system of equations does not have a solution.