What is the solution set of the equations x + y = 5 and x + y = 10?

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Question: What is the solution set of the equations x + y = 5 and x + y = 10?

Options:

Correct Answer: No solution

Solution:

The two equations represent parallel lines, which means they do not intersect and thus have no solution.

What is the solution set of the equations x + y = 5 and x + y = 10?

What is the solution set of the equations x + y = 5 and x + y = 10?

Step 1: Understand that the equations x + y = 5 and x + y = 10 represent lines on a graph.
Step 2: Rewrite the first equation as y = 5 - x. This shows the line where the sum of x and y equals 5.
Step 3: Rewrite the second equation as y = 10 - x. This shows the line where the sum of x and y equals 10.
Step 4: Notice that both equations have the same slope (they are both in the form y = mx + b). This means they are parallel lines.
Step 5: Since parallel lines never meet, they do not have any points in common.
Step 6: Conclude that there is no solution to the equations because they do not intersect.

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