help with solving system of equations

Question

  3x + 4y + z = 7

          2y + z = 3

-5x + 3y + 8z = -31

 

 

thanks

Answer 1

3x + 4y + z = 7                first elimination: y = (3-z)/2; plug this in equations 1 and 5. then multiply equation

        2y + z = 3                1 by 5 and equation 3 by 3 and after replacing y obtained from the first elimination

-5x + 3y + 8z =-31            we get and adding up equations 1 and 3 modified

 

29((3-z)/2) +29 = -58

this will lead us to (3-z+2z)/2 = -2

solving, the result is that z = -7.

solving for y we obtain that y= (3+7)/2 = 5

and then solve for x.