General Solution-Three variables-Two Equations

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To find the general solution for the equations u − w + y = 1 and u + w + 2y = 0, one approach is to recognize that each equation represents a plane in three-dimensional space, and their intersection forms a line. To determine the direction of this line, one can use methods such as elimination or substitution to express one variable in terms of the others. This will lead to a parametric representation of the line, which can be expressed in the form (u,w,y) = (a,b,c) + k*(d,e,f). Understanding the geometric interpretation of the equations aids in visualizing the solution. The discussion emphasizes the importance of identifying the direction vector for the line of intersection.
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Homework Statement



Find the general solution of the following set of equations:

u − w + y = 1
u + w + 2y = 0

Homework Equations





The Attempt at a Solution



I know that the solution is in this form (u,w,y)= (a,b,c) + k*(d,e,f)

Can you please explain me how i am going to find it?
 
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hi mikael27! :smile:

there are several ways to do this

one is to see that each equation represents a plane (in ordinary 3D space)

so their intersection is a line …

how would you find the direction of that line? :wink:​
 

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