Are Two Equivalent Linear Systems with Different Solution Sets Possible? | A Math Explanation

Is the statement​ Two equivalent linear systems can have different solution​ sets true or​ false? Explain.

False, because two systems are called equivalent if they have the same solution set.

The statement Two equivalent linear systems can have different solution sets is false.

Two linear systems are called equivalent if they have the same solution set. This means that they differ only by the notation of their equations.

If two linear systems are equivalent, it means that they have the same coefficients for their variables and the same constants on the right side of their equations. Therefore, they will produce the same solution set.

For example, consider the following two equivalent systems:

2x + 3y = 5
4x + 6y = 10

and

1x + (3/2)y = 2.5
2x + 3y = 5

Both systems are equivalent since the equations in the second system are obtained from the first system by dividing the first equation by 2 and the second equation by 2, thus keeping all coefficients the same. Thus, they have exactly the same solution set, which is {(1, 1)}.

Therefore, the statement Two equivalent linear systems can have different solution sets is false.

More Answers: