Choose a related problem about a healthy lifestyle in daily life that involves a system of linear equations with four variables. Convert the problem selected to mathematical sentences. Solve the system of linear equations using two methods, including the Gauss-Jordan elimination method.

Is this statement true or false? In a system of linear equations, multiplying one equation by a non-zero real number can change the number of solutions to the system.

How many solutions are there to a system of linear equations if the lines are perpendicular and they have the same y-intercept?

Exercise 1. A student is asked to prove If m is even and n is odd, then m² +n² is odd. The student provides the following proof: Proof. If m is even and n is odd, then m² + n² is odd. Since m is even, m = = 2k for any integer k. Since n is odd, n = 2k + 1. Note that m² + n² = (2k)² + (2k + 1)² = 8k² + 4k +1 So m² + n² is odd because it is an even number plus 1. (a) Identify the errors in the proof above. There are multiple errors. Explain each error. Your explanation should be written to the student who made the error and should try to help the student understand why what they wrote is incorrect. (b) In addition to errors, provide suggestions to improve the student's proof writing. That is, explain what parts of the proof are unclear or unjustified. Explain how such parts of the proof prevent some students from fully following the ment made. (c) Finally, provide a correct proof of the theorem above.