Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 08
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Question A 08 

Find all solutions to the linear system

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Represent the system of the linear equations as an augmented matrix. 
Hint 2 

Note that the elementary row operations do not change the solution to the linear system 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The given system of the linear equations can be represented by the augmented matrix:
Since elementary row operations do not change the solution to the linear system, we remove the entry in column 1 of row 2 by subtracting off 2 times the first row;
which is equivalent to
And the third equation implies , so . Finally, from the first equation, we obtain . Therefore, the solution is . 