Why are the systems equivalent?

1. What does it mean for a system to be equivalent?
2. How do you know if systems are equivalent?
3. What linear systems are equivalent?

What does it mean for a system to be equivalent?

Systems of equations that have the same solution are called equivalent systems. Given a system of two equations, we can produce an equivalent system by replacing one equation by the sum of the two equations, or by replacing an equation by a multiple of itself.

How do you know if systems are equivalent?

Two systems of linear equations are equivalent if and only if they have the same set of solutions. In other words, two systems are equivalent if and only if every solution of one of them is also a solution of the other.

What linear systems are equivalent?

Two linear systems are called equivalent if they have the same solution set. That is, each solution of the first system is a solution to the second system, and vice versa. , as you easily can see on Figure 1.