Question

Question Identify the pair of linear equations that have the same solution set.(1 point)

Answer 1

To identify a pair of linear equations that have the same solution set, we often look for equations that are proportional to each other. This can be done by checking if one equation can be obtained from the other by multiplying or dividing by a constant.

For example, consider the following pairs of linear equations:

1. \(2x + 4y = 8\) and \(x + 2y = 4\)
2. \(3x - 6y = 9\) and \(6x - 12y = 18\)
3. \(x - 2y = 3\) and \(2x - 4y = 6\)

In each of these cases, the second equation is a multiple of the first.

1. In the first pair, dividing the first equation by 2 gives the second equation.
2. In the second pair, dividing the first equation by 3 gives the second equation.
3. In the third pair, dividing the second equation by 2 gives the first equation.

All pairs above represent the same line on a graph, meaning they have the same solution set.

Therefore, any of these pairs (or others that meet the same condition) would be valid answers for your question. If you have specific pairs in mind you’d like to compare, please provide them!