Question

A student solved an equation and found that the variable was eliminated in the process of solving the equation. How would the student know whether the equation is an identity or an equation with no solution?

Answer 1

if the student got a true statement, it is an identity
example, ending with x=x or 10=10 means it is an identity

if the student ended up with a false statement, there is no solution
example, 10=2

Answer 2

In elimination method we eliminate one variable by multiplying constant and adding/subtracting with the other equation.

But sometimes it happen that the result after applying elimination method eliminate both the variables and we get either true statement (like 0 = 0) or a false statement (like 0 = 6). If we get false statement then the given set of equations has no solution.

Let’s look at an example.

Solve for x and y.

-x – y = -4

and, x + y = 2

After subtracting equation first equation from second one. We get,

0 = −2

Hence, There is no solution.