Question

Two systems of equations are shown. Which TWO of the following statements each provide sufficient reasoning to show that the systems have the same solution?

a) Both systems have the same coefficients for x and y.
b) Both systems have the same solutions for x and y.
c) Both systems have the same y-intercepts.
d) Both systems have the same slopes.

Answer 1

The two statements that provide sufficient reasoning for showing that two systems of equations have the same solution are: 1) Both systems have the same solutions for x and y, and 2) Both systems have the same slopes.

Step-by-step explanation:

To show that two systems of equations have the same solution, we need to look for statements that provide sufficient reasoning. In this case, the two statements that provide sufficient reasoning are:

1. Both systems have the same solutions for x and y.
2. If the two systems have the same solutions, then they must have the same solution.
3. Both systems have the same slopes.
4. If the slopes of the two systems are the same, then the lines represented by the systems are parallel and will never intersect, which means they have the same solution.