Solve the following linear systems:

Question

7x-y-3z=1

4x+5y+z=0

2x-y+2z=3

Answer 1

One way of solving a 3 by 3 system is by solving for a convenient variable and then replacing it in the other equations.

 

So, using the first equation, it is easy to solve for y....getting y=7x-3z-1   now substitute in eq 2 and eq 3 to get

 

4x + 5(7x-3z-1) +z = 0 and

2x -(7x-3z-1) + 2z = 3

 

This simplifies down to

39x-14z =5    and

-5x+5z =2

 

You now have a 2 by 2 system of equations to solve which I hope you can do.  I got a final answer which I checked that comes out to be x=.424, y= -.504 and z=.824.

 

Hope this helped.