System of equations

Question

Solve the system and if an infinite number of solutions exist,  write the solution set in terms of one free variable

 

2x-3y+z=-2

-4x+9y=7

Answer 1

Multiplies the top equation by 2:

  4x - 6y + 2z = -4

 

Adds it to the second equation:

 

   3y + 2z = 3

 

  3y = 3 - 2z

 

  y = (3-2z)/3

 

Plugs into the second equation:

 

  -4x + 9(3-2z)/3 = 7

 

 -4x + 3(3-2z) = 7

 

  -4x + 9 - 6z = 7

 

  -4x = 6z - 2

 

   x = (-3/2)z + (1/2)

 

CHECK:

  2[ (-3/2)z + (1/2) ] - 3 (3 - 2z)/3 + z = 

    -3z + 1 - 3 + 2z + z = -2

 

-4 [ (-3/2)z + (1/2)] + 9 ( 3 - 2z)/3 =

  6z - 2 + 9 - 6z = 7