Question

The system of equations is solved using the linear combination method. What does 0 = −12 mean regarding the solution to the system?

Answer 1

0=-12 is not true.

What this means is that there is no solution, and that the equation will always be false no matter the value of the variable.

Answer 2

0= -12 means that the system of equations has no solution.

Explanation:

While solving a system of linear equation.

There are three possibilities--

a)

Unique solution or one solution--

It is obtained when we get a unique value for our variable.

For example if we get:

x=5

b)

Infinite many solution--

It is obtained when we get a equality which is true but do not get a particular value of x.

i.e. the system is true for infinite values of x.

for example if we get equality such as:

0=0

or 12=12 and so.

c)

No Solution--

It is a condition when at the end we get a equality which is false.

for example a non-zero number equal to 0 is a false statement and hence we get a no- solution.

Here we have:

0= -12

i.e. a non zero number i.e. -12 is equal to zero.

Hence, the solution to the system is No solution.