Science:Math Exam Resources/Courses/MATH200/December 2012/Question 01 (a)
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Question 01 (a) 

Let be the line of intersection of the planes and (a) Find the points in which the line intersects the coordinate planes. 
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 

First, find the parametric equation of the line . Therefore, express the variables and in terms of , using the two plane equations. 
Hint 2 

Once you have the parametric equation for with parameter , set the first entry of equal to . Solve for and plug in your result as in . Then you find the point, where intersects the plane. 
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 line satisfies both plane equations. We solve the second one for :
and plug the result into the first equation:
Then the line is
So, intersects with the plane in the point
In the plane, . Hence, for the second entry of the line holds when So, intersects with the plane in the point
So, intersects with the plane in the point
