SOLUTION: Please help me solve this equation: Solve the system of equations. 3x−4y−7z = −6 2x+3y−5z = 1 (If the system is dependent, enter a general solution in terms of c.

Algebra ->  Systems-of-equations -> SOLUTION: Please help me solve this equation: Solve the system of equations. 3x−4y−7z = −6 2x+3y−5z = 1 (If the system is dependent, enter a general solution in terms of c.      Log On


   

Question 1156489: Please help me solve this equation:
Solve the system of equations.
3x−4y−7z = −6
2x+3y−5z = 1
(If the system is dependent, enter a general solution in terms of c.)
Answer by greenestamps(13330) About Me  (Show Source):
You can put this solution on YOUR website!


There are three variables and only two equations. Therefore we can't get a single solution; we can only get a family of solutions in terms of some parameter.

The process is straightforward, although the calculations are generally a bit ugly.

(1) Use elimination to reduce the system of 2 equations and 3 unknowns to a system of 1 equation with 2 unknowns.
(2) Solve that single equation for one variable in terms of the other.
(3) Substitute into either of the original equations to find an expression for the third variable.

(1) I chose to eliminate x: multiply the first equation by 2 and the second equation by -3 and add:
  6x - 8y - 14z = -12
 -6x - 9y + 15z = -3
 ---------------------
     -17y +  z  = -15

Solve for z in terms of y:
             z = 17y - 15

(3) Substitute y for y and 17y-15 for z in one of the original equations to find x in terms of y:

2x%2B3y-5%2817y-15%29+=+1

2x%2B3y-85y%2B75+=+1

2x+=+82y-74

x+=+41y-37

ANSWER:
x = 41y-37; y = y; z = 17y - 15

Choose any number for the "parameter" y and use it to find values for x and z. Those values of x, y, and z will satisfy both of the given equations.