SOLUTION: Solve the system of linear equations (set z=a if dependent) I tried the problem below but I'm clearly missing something: Eqn 1: {{{10x-3y+2z=-18}}} Eqn 2: {{{19x-5y-z=13}}}

Algebra ->  Equations -> SOLUTION: Solve the system of linear equations (set z=a if dependent) I tried the problem below but I'm clearly missing something: Eqn 1: {{{10x-3y+2z=-18}}} Eqn 2: {{{19x-5y-z=13}}}       Log On


   

Question 377170: Solve the system of linear equations (set z=a if dependent)
I tried the problem below but I'm clearly missing something:
Eqn 1: 10x-3y%2B2z=-18
Eqn 2: 19x-5y-z=13
2(Eqn 1) - Eqn 2
20x+-+6y+%2B+4z+=+-36
19x+-+5y+-+z+=+13
Eqn 1 = x - 11y + 3z = -23
-19(Eqn 1) + Eqn 2
-19x+%2B+209y+-+57z+=+437
19x+-+5y+-z+=+13
Eqn 1 = 204y+-+58z+=+450
Let z = 2a
I'm getting y=%2875%2F34%29+%2B+%2829%2F51%29a and that is not right. Did not solve further. Any help you can provide is appreciated!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
With 3 variables and 2 equations, you can eliminate any of the 3 variables and get the equation of a line.
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An equation in 3 variables is a plane in 3-space. The 2 eqns are of 2 planes, and their intersection, which is a line in 3-space.
By eliminating the x, you get the projection of the line onto the y-z plane.
By eliminating the y, you get the projection of the line onto the x-z plane.
By eliminating the z, you get the projection of the line onto the x-y plane.