how to solve equation in term of z

Question

solve the following system of equation in the terms of z

 

1. x+2y-2z=3

2. 3x+y+z=8

Answer 1

Multiply the first equation by -3:  -3x-6y+6z = -9

                                                3x+y +z  = 8

 

Add the equations to get -5y + 7z = -1

                               

                                     So, y = (7/5)z + 1/5

 

From equation 1 we then have x + 2[(7/5)z + 1/5] - 2z = 3

 

                                           x + (14/5)z + 2/5 - 2z = 3

 

                                                                       x = (-4/5)z + 13/5

 

Solution set:  x = (-4/5)z + 13/5

                    y = (7/5)z + 1/5

                    z = any real number